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%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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currentdict end
currentfile eexec
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%%CreationDate: 1991 Aug 20 16:36:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
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/FontName /CMBX8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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readonly def
/FontBBox{-59 -250 1235 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX5
%!PS-AdobeFont-1.1: CMBX5 1.0
%%CreationDate: 1991 Aug 20 16:35:12
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 97 /a put
readonly def
/FontBBox{-40 -250 1483 756}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX7
%!PS-AdobeFont-1.1: CMBX7 1.0
%%CreationDate: 1991 Aug 20 16:35:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 90 /Z put
dup 97 /a put
readonly def
/FontBBox{-55 -250 1289 751}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 80 /summationtext put
dup 88 /summationdisplay put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 77 /M put
dup 83 /S put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI8
%!PS-AdobeFont-1.1: CMTI8 1.0
%%CreationDate: 1991 Aug 18 21:07:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 44 /comma put
dup 45 /hyphen put
dup 65 /A put
dup 67 /C put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 77 /M put
dup 79 /O put
dup 81 /Q put
dup 83 /S put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-35 -250 1190 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 19 /acute put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 88 /X put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 109 /m put
dup 112 /p put
readonly def
/FontBBox{37 -250 1349 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 14 /ffi put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 53 /five put
dup 58 /colon put
dup 59 /semicolon put
dup 65 /A put
dup 70 /F put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /prime put
readonly def
/FontBBox{21 -944 1448 791}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 23 /nu put
dup 59 /comma put
dup 60 /less put
dup 66 /B put
dup 69 /E put
dup 73 /I put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 117 /u put
dup 122 /z put
readonly def
/FontBBox{0 -250 1171 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 10 /Omega put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 20 /lessequal put
dup 48 /prime put
dup 50 /element put
dup 54 /negationslash put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 8 /circleplus put
dup 14 /openbullet put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 26 /propersubset put
dup 27 /propersuperset put
dup 33 /arrowright put
dup 50 /element put
dup 54 /negationslash put
dup 55 /mapsto put
dup 59 /emptyset put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 116 /unionsq put
dup 120 /section put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 30 /phi put
dup 32 /psi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 81 /Q put
dup 84 /T put
dup 85 /U put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 118 /v put
dup 120 /x put
dup 122 /z put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 19 /acute put
dup 22 /macron put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 126 /tilde put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 71 /G put
dup 76 /L put
dup 82 /R put
dup 99 /c put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 110 /n put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 122 /z put
readonly def
/FontBBox{14 -250 1077 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 90 /Z put
dup 97 /a put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 121 /y put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
currentdict end
currentfile eexec
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Fs(1,)p eop end
%%Page: 10 10
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Fr(f)5 b(;)119 b(c)22 b Fs(+)g Fr(d)28 b Fq(\025)g Fr(b)22
b Fs(+)h Fr(e)p Fl(;)0 5384 y Fs(\(e\))1094 b Fr(F)1294
5333 y Fo(\()p Fn(a)p Fo(\))1280 5412 y Fn(j)1405 5384
y Fr(F)1483 5333 y Fo(\()p Fn(b)p Fo(\))1469 5412 y Fn(i)1585
5384 y Fr(F)1663 5333 y Fo(\()p Fn(c)p Fo(\))1649 5412
y Fn(j)1766 5384 y Fr(F)1844 5333 y Fo(\()p Fn(d)p Fo(\))1830
5414 y Fn(k)1952 5384 y Fr(F)2030 5333 y Fo(\()p Fn(e)p
Fo(\))2016 5412 y Fn(j)2135 5384 y Fr(F)2213 5333 y Fo(\()p
Fn(f)8 b Fo(\))2199 5412 y Fn(i)p eop end
%%Page: 11 11
TeXDict begin 11 10 bop 414 50 a Fi(TIGHT)39 b(MONOMIALS)e(IN)g
(QUANTIZED)h(ENVELOPING)f(ALGEBRAS)368 b(11)0 289 y Fl(for)35
b Fr(c)22 b Fs(+)h Fr(e)28 b Fq(\025)g Fr(b)22 b Fs(+)h
Fr(f)5 b(;)118 b(b)27 b Fq(\025)h Fr(a)22 b Fs(+)h Fr(c;)118
b(d)28 b Fq(\025)g Fr(c)22 b Fs(+)h Fr(e)p Fl(;)0 642
y Fs(\(f\))1108 b Fr(F)1294 590 y Fo(\()p Fn(a)p Fo(\))1280
670 y Fn(j)1405 642 y Fr(F)1483 590 y Fo(\()p Fn(b)p
Fo(\))1469 672 y Fn(k)1585 642 y Fr(F)1663 590 y Fo(\()p
Fn(c)p Fo(\))1649 670 y Fn(j)1766 642 y Fr(F)1844 590
y Fo(\()p Fn(d)p Fo(\))1830 670 y Fn(i)1952 642 y Fr(F)2030
590 y Fo(\()p Fn(e)p Fo(\))2016 670 y Fn(j)2135 642 y
Fr(F)2213 590 y Fo(\()p Fn(f)8 b Fo(\))2199 672 y Fn(k)0
876 y Fl(for)35 b Fr(c)22 b Fs(+)h Fr(e)28 b Fq(\025)g
Fr(b)22 b Fs(+)h Fr(f)5 b(;)118 b(b)27 b Fq(\025)h Fr(a)22
b Fs(+)h Fr(c;)118 b(d)28 b Fq(\025)g Fr(c)22 b Fs(+)h
Fr(e)p Fl(;)0 1230 y Fs(\(g\))1088 b Fr(F)1294 1178 y
Fo(\()p Fn(f)8 b Fo(\))1280 1257 y Fn(i)1408 1230 y Fr(F)1486
1178 y Fo(\()p Fn(e)p Fo(\))1472 1257 y Fn(j)1591 1230
y Fr(F)1669 1178 y Fo(\()p Fn(d)p Fo(\))1655 1260 y Fn(k)1778
1230 y Fr(F)1856 1178 y Fo(\()p Fn(c)p Fo(\))1842 1257
y Fn(j)1958 1230 y Fr(F)2036 1178 y Fo(\()p Fn(b)p Fo(\))2022
1257 y Fn(i)2139 1230 y Fr(F)2217 1178 y Fo(\()p Fn(a)p
Fo(\))2203 1257 y Fn(j)0 1464 y Fl(for)35 b Fr(c)22 b
Fs(+)h Fr(e)28 b Fq(\025)g Fr(b)22 b Fs(+)h Fr(f)5 b(;)118
b(b)27 b Fq(\025)h Fr(a)22 b Fs(+)h Fr(c;)118 b(d)28
b Fq(\025)g Fr(c)22 b Fs(+)h Fr(e)p Fl(;)0 1817 y Fs(\(h\))1083
b Fr(F)1294 1765 y Fo(\()p Fn(f)8 b Fo(\))1280 1847 y
Fn(k)1408 1817 y Fr(F)1486 1765 y Fo(\()p Fn(e)p Fo(\))1472
1845 y Fn(j)1591 1817 y Fr(F)1669 1765 y Fo(\()p Fn(d)p
Fo(\))1655 1845 y Fn(i)1778 1817 y Fr(F)1856 1765 y Fo(\()p
Fn(c)p Fo(\))1842 1845 y Fn(j)1958 1817 y Fr(F)2036 1765
y Fo(\()p Fn(b)p Fo(\))2022 1847 y Fn(k)2139 1817 y Fr(F)2217
1765 y Fo(\()p Fn(a)p Fo(\))2203 1845 y Fn(j)0 2052 y
Fl(for)35 b Fr(c)22 b Fs(+)h Fr(e)28 b Fq(\025)g Fr(b)22
b Fs(+)h Fr(f)5 b(;)118 b(b)27 b Fq(\025)h Fr(a)22 b
Fs(+)h Fr(c;)118 b(d)28 b Fq(\025)g Fr(c)22 b Fs(+)h
Fr(e)p Fl(.)120 2230 y Fs(The)33 b(pro)s(of)h(is)f(an)g(application)g
(of)h(Corollary)d(10.)44 b(W)-8 b(e)33 b(\014rst)h(consider)g(case)g
(\(a\).)120 2349 y(Let)f Fu(i)28 b Fs(=)g(\()p Fr(i)536
2364 y Fo(1)580 2349 y Fr(;)17 b(i)659 2364 y Fo(2)704
2349 y Fr(;)g(i)783 2364 y Fo(3)827 2349 y Fr(;)g(i)906
2364 y Fo(4)950 2349 y Fr(;)g(i)1029 2364 y Fo(5)1074
2349 y Fr(;)g(i)1153 2364 y Fo(6)1197 2349 y Fs(\))27
b(=)i(\()p Fr(i;)17 b(k)s(;)g(j;)g(i;)g(k)s(;)g(j)6 b
Fs(\).)40 b(Let)33 b Fu(a)28 b Fs(=)g(\()p Fr(a)2465
2364 y Fo(1)2509 2349 y Fr(;)17 b(a)2607 2364 y Fo(2)2651
2349 y Fr(;)g(a)2749 2364 y Fo(3)2792 2349 y Fr(;)g(a)2890
2364 y Fo(4)2934 2349 y Fr(;)g(a)3032 2364 y Fo(5)3076
2349 y Fr(;)g(a)3174 2364 y Fo(6)3217 2349 y Fs(\).)120
2469 y(No)m(w)383 2444 y(\026)361 2469 y Fr(P)61 b Fs(is)47
b(three)h(dimensional)g(with)f(the)g(co)s(ordinate)h(functions)g
Fr(z)2852 2484 y Fn(i)2937 2469 y Fs(=)k Fr(z)3116 2433
y Fo(14)3112 2495 y Fn(i)3252 2469 y Fs(=)g Fr(z)3431
2433 y Fo(41)3427 2495 y Fn(i)3516 2469 y Fs(,)0 2588
y Fr(z)46 2603 y Fn(k)123 2588 y Fs(=)28 b Fr(z)278 2552
y Fo(25)274 2616 y Fn(k)391 2588 y Fs(=)g Fr(z)546 2552
y Fo(52)542 2616 y Fn(k)664 2588 y Fs(and)34 b Fr(z)904
2603 y Fn(j)974 2588 y Fs(=)28 b Fr(z)1129 2552 y Fo(36)1125
2614 y Fn(j)1242 2588 y Fs(=)g Fr(z)1397 2552 y Fo(63)1393
2614 y Fn(j)1482 2588 y Fs(.)120 2719 y(The)33 b(non-homogeneous)i
(quadratic)e(form)h(on)1969 2694 y(\026)1947 2719 y Fr(P)47
b Fs(is)0 2953 y Fr(z)50 2912 y Fo(2)46 2978 y Fn(i)107
2953 y Fs(+)12 b Fr(z)246 2912 y Fo(2)242 2978 y Fn(j)303
2953 y Fs(+)g Fr(z)442 2912 y Fo(2)438 2978 y Fn(k)499
2953 y Fq(\000)g Fr(z)634 2968 y Fn(i)668 2953 y Fr(z)714
2968 y Fn(j)767 2953 y Fq(\000)g Fr(z)902 2968 y Fn(j)945
2953 y Fr(z)991 2968 y Fn(k)1052 2953 y Fs(+)g(\()p Fr(a)1233
2968 y Fo(3)1288 2953 y Fq(\000)g Fr(a)1430 2968 y Fo(1)1486
2953 y Fq(\000)g Fr(a)1628 2968 y Fo(4)1673 2953 y Fs(\))p
Fr(z)1758 2968 y Fn(i)1803 2953 y Fs(+)g(\()p Fr(a)1984
2968 y Fo(3)2039 2953 y Fq(\000)g Fr(a)2181 2968 y Fo(2)2237
2953 y Fq(\000)g Fr(a)2379 2968 y Fo(5)2424 2953 y Fs(\))p
Fr(z)2509 2968 y Fn(k)2569 2953 y Fs(+)g(\()p Fr(a)2750
2968 y Fo(4)2806 2953 y Fs(+)g Fr(a)2948 2968 y Fo(5)3004
2953 y Fq(\000)g Fr(a)3146 2968 y Fo(3)3202 2953 y Fq(\000)g
Fr(a)3344 2968 y Fo(6)3389 2953 y Fs(\))p Fr(z)3474 2968
y Fn(j)3516 2953 y Fr(:)0 3187 y Fs(If)684 3306 y Fr(a)737
3321 y Fo(3)809 3306 y Fq(\025)29 b Fr(a)968 3321 y Fo(1)1034
3306 y Fs(+)23 b Fr(a)1187 3321 y Fo(4)1231 3306 y Fr(;)116
b(a)1428 3321 y Fo(3)1500 3306 y Fq(\025)28 b Fr(a)1658
3321 y Fo(2)1725 3306 y Fs(+)22 b Fr(a)1877 3321 y Fo(5)1922
3306 y Fr(;)115 b(a)2118 3321 y Fo(4)2185 3306 y Fs(+)23
b Fr(a)2338 3321 y Fo(5)2410 3306 y Fq(\025)28 b Fr(a)2568
3321 y Fo(3)2634 3306 y Fs(+)23 b Fr(a)2787 3321 y Fo(6)2831
3306 y Fr(;)0 3493 y Fs(then)31 b(the)g(quadratic)f(form)h(tak)m(es)f
(a)g(v)-6 b(alue)31 b Fr(>)d Fs(0)i(at)g(\()p Fr(z)2045
3508 y Fn(i)2078 3493 y Fr(;)17 b(z)2169 3508 y Fn(j)2211
3493 y Fr(;)g(z)2302 3508 y Fn(k)2350 3493 y Fs(\))31
b(with)f Fr(z)2690 3508 y Fn(i)2751 3493 y Fq(\025)e
Fs(0)p Fr(;)17 b(z)2997 3508 y Fn(j)3066 3493 y Fq(\025)28
b Fs(0)p Fr(;)17 b(z)3312 3508 y Fn(k)3388 3493 y Fq(\025)28
b Fs(0)0 3635 y(\(not)33 b(all)f(three)i(zero\);)f(hence)i(the)e
(monomial)g Fr(F)1872 3584 y Fo(\()p Fn(a)1946 3594 y
Fk(1)1985 3584 y Fo(\))1858 3663 y Fn(i)2021 3635 y Fr(F)2099
3584 y Fo(\()p Fn(a)2173 3594 y Fk(2)2212 3584 y Fo(\))2085
3665 y Fn(k)2248 3635 y Fr(F)2326 3584 y Fo(\()p Fn(a)2400
3594 y Fk(3)2439 3584 y Fo(\))2312 3663 y Fn(j)2476 3635
y Fr(F)2554 3584 y Fo(\()p Fn(a)2628 3594 y Fk(4)2667
3584 y Fo(\))2540 3663 y Fn(i)2703 3635 y Fr(F)2781 3584
y Fo(\()p Fn(a)2855 3594 y Fk(5)2894 3584 y Fo(\))2767
3665 y Fn(k)2930 3635 y Fr(F)3008 3584 y Fo(\()p Fn(a)3082
3594 y Fk(6)3121 3584 y Fo(\))2994 3663 y Fn(j)3191 3635
y Fs(is)g(tigh)m(t.)120 3761 y(Next)f(w)m(e)i(consider)g(case)g(\(c\).)
120 3881 y(Let)j Fu(i)d Fs(=)h(\()p Fr(i)553 3896 y Fo(1)597
3881 y Fr(;)17 b(i)676 3896 y Fo(2)721 3881 y Fr(;)g(i)800
3896 y Fo(3)844 3881 y Fr(;)g(i)923 3896 y Fo(4)967 3881
y Fr(;)g(i)1046 3896 y Fo(5)1091 3881 y Fr(;)g(i)1170
3896 y Fo(6)1214 3881 y Fs(\))34 b(=)g(\()p Fr(i;)17
b(j;)g(i;)g(k)s(;)g(j;)g(i)p Fs(\).)53 b(Let)38 b Fu(a)33
b Fs(=)i(\()p Fr(a)2497 3896 y Fo(1)2541 3881 y Fr(;)17
b(a)2639 3896 y Fo(2)2683 3881 y Fr(;)g(a)2781 3896 y
Fo(3)2824 3881 y Fr(;)g(a)2922 3896 y Fo(4)2966 3881
y Fr(;)g(a)3064 3896 y Fo(5)3108 3881 y Fr(;)g(a)3206
3896 y Fo(6)3249 3881 y Fs(\).)56 b(The)0 4001 y(non-homogeneous)35
b(quadratic)e(form)g(on)1645 3975 y(\026)1623 4001 y
Fr(P)47 b Fs(is)56 4234 y Fq(\000)22 b Fr(z)205 4193
y Fo(31)201 4259 y Fn(i)290 4234 y Fr(z)340 4193 y Fo(52)336
4259 y Fn(j)448 4234 y Fq(\000)g Fr(z)597 4193 y Fo(36)593
4259 y Fn(i)682 4234 y Fr(z)732 4193 y Fo(25)728 4259
y Fn(j)840 4234 y Fs(+)g Fr(z)989 4193 y Fo(31)985 4259
y Fn(i)1074 4234 y Fr(z)1124 4193 y Fo(63)1120 4259 y
Fn(i)1232 4234 y Fs(+)g Fr(z)1381 4193 y Fo(36)1377 4259
y Fn(i)1466 4234 y Fr(z)1516 4193 y Fo(16)1512 4259 y
Fn(i)1624 4234 y Fs(+)g Fr(z)1773 4193 y Fo(16)1769 4259
y Fn(i)1858 4234 y Fr(z)1908 4193 y Fo(13)1904 4259 y
Fn(i)2016 4234 y Fs(+)g(\()p Fr(z)2204 4193 y Fo(13)2200
4259 y Fn(i)2289 4234 y Fs(\))2328 4193 y Fo(2)2395 4234
y Fs(+)g(\()p Fr(z)2583 4193 y Fo(16)2579 4259 y Fn(i)2668
4234 y Fs(\))2707 4193 y Fo(2)2774 4234 y Fs(+)g(\()p
Fr(z)2962 4193 y Fo(36)2958 4259 y Fn(i)3047 4234 y Fs(\))3086
4193 y Fo(2)3153 4234 y Fs(+)g(\()p Fr(z)3341 4193 y
Fo(25)3337 4259 y Fn(j)3426 4234 y Fs(\))3465 4193 y
Fo(2)56 4400 y Fs(+)g(\()p Fr(a)247 4415 y Fo(2)314 4400
y Fq(\000)g Fr(a)466 4415 y Fo(1)533 4400 y Fq(\000)g
Fr(a)685 4415 y Fo(3)730 4400 y Fs(\))p Fr(z)819 4359
y Fo(31)815 4424 y Fn(i)926 4400 y Fs(+)g(\()p Fr(a)1117
4415 y Fo(2)1183 4400 y Fs(+)h Fr(a)1336 4415 y Fo(5)1403
4400 y Fq(\000)f Fr(a)1555 4415 y Fo(1)1622 4400 y Fq(\000)g
Fs(2)p Fr(a)1824 4415 y Fo(3)1891 4400 y Fq(\000)g Fr(a)2043
4415 y Fo(6)2088 4400 y Fs(\))p Fr(z)2177 4359 y Fo(61)2173
4424 y Fn(i)2284 4400 y Fs(+)g(\()p Fr(a)2475 4415 y
Fo(5)2542 4400 y Fq(\000)g Fr(a)2694 4415 y Fo(3)2761
4400 y Fq(\000)g Fr(a)2913 4415 y Fo(6)2958 4400 y Fs(\))p
Fr(z)3047 4359 y Fo(63)3043 4424 y Fn(i)56 4566 y Fs(+)g(\()p
Fr(a)247 4581 y Fo(3)314 4566 y Fs(+)g Fr(a)466 4581
y Fo(4)533 4566 y Fq(\000)g Fr(a)685 4581 y Fo(2)752
4566 y Fq(\000)g Fr(a)904 4581 y Fo(5)949 4566 y Fs(\))p
Fr(z)1038 4525 y Fo(52)1034 4590 y Fn(j)1123 4566 y Fr(:)0
4799 y Fs(There)i(are)f(5)f(indep)s(enden)m(t)j(v)-6
b(ariables:)39 b(the)23 b(8)g(v)-6 b(ariables)23 b(ab)s(o)m(v)m(e)g
(satisfy)f(the)h(linear)g(relations:)496 5033 y Fr(z)546
4992 y Fo(13)542 5057 y Fn(i)653 5033 y Fs(+)f Fr(z)802
4992 y Fo(63)798 5057 y Fn(i)915 5033 y Fs(=)28 b Fr(z)1070
4992 y Fo(31)1066 5057 y Fn(i)1178 5033 y Fs(+)22 b Fr(z)1327
4992 y Fo(36)1323 5057 y Fn(i)1412 5033 y Fr(;)116 b(z)1606
4992 y Fo(16)1602 5057 y Fn(i)1714 5033 y Fs(+)22 b Fr(z)1863
4992 y Fo(13)1859 5057 y Fn(i)1976 5033 y Fs(=)28 b Fr(z)2131
4992 y Fo(61)2127 5057 y Fn(i)2238 5033 y Fs(+)23 b Fr(z)2388
4992 y Fo(63)2384 5057 y Fn(i)2473 5033 y Fr(;)116 b(z)2667
4992 y Fo(25)2663 5057 y Fn(j)2780 5033 y Fs(=)28 b Fr(z)2935
4992 y Fo(52)2931 5057 y Fn(j)3020 5033 y Fr(:)120 5266
y Fs(If)684 5386 y Fr(a)737 5401 y Fo(2)809 5386 y Fq(\025)h
Fr(a)968 5401 y Fo(1)1034 5386 y Fs(+)23 b Fr(a)1187
5401 y Fo(3)1231 5386 y Fr(;)116 b(a)1428 5401 y Fo(5)1500
5386 y Fq(\025)28 b Fr(a)1658 5401 y Fo(3)1725 5386 y
Fs(+)22 b Fr(a)1877 5401 y Fo(6)1922 5386 y Fr(;)115
b(a)2118 5401 y Fo(3)2185 5386 y Fs(+)23 b Fr(a)2338
5401 y Fo(4)2410 5386 y Fq(\025)28 b Fr(a)2568 5401 y
Fo(2)2634 5386 y Fs(+)23 b Fr(a)2787 5401 y Fo(5)2831
5386 y Fr(;)p eop end
%%Page: 12 12
TeXDict begin 12 11 bop 0 50 a Fi(12)1419 b(G.)37 b(LUSZTIG)0
289 y Fs(then)h(the)f(quadratic)g(form)g(tak)m(es)g(v)-6
b(alues)37 b Fr(>)e Fs(0)h(on)2017 264 y(\026)1995 289
y Fr(P)2073 253 y Fo(+)2163 289 y Fq(\000)25 b(f)p Fs(0)p
Fq(g)p Fs(,)37 b(hence)i(the)e(corresp)s(onding)0 408
y(monomial)32 b(is)i(tigh)m(t.)120 528 y(Next)e(w)m(e)i(consider)g
(case)g(\(e\).)120 648 y(Let)j Fu(i)c Fs(=)h(\()p Fr(i)551
663 y Fo(1)596 648 y Fr(;)17 b(i)675 663 y Fo(2)719 648
y Fr(;)g(i)798 663 y Fo(3)842 648 y Fr(;)g(i)921 663
y Fo(4)966 648 y Fr(;)g(i)1045 663 y Fo(5)1089 648 y
Fr(;)g(i)1168 663 y Fo(6)1212 648 y Fs(\))33 b(=)h(\()p
Fr(j;)17 b(i;)g(j;)g(k)s(;)g(j;)g(i)p Fs(\).)52 b(Let)37
b Fu(a)c Fs(=)h(\()p Fr(a)2498 663 y Fo(1)2542 648 y
Fr(;)17 b(a)2640 663 y Fo(2)2684 648 y Fr(;)g(a)2782
663 y Fo(3)2826 648 y Fr(;)g(a)2924 663 y Fo(4)2967 648
y Fr(;)g(a)3065 663 y Fo(5)3109 648 y Fr(;)g(a)3207 663
y Fo(6)3251 648 y Fs(\).)54 b(The)0 767 y(non-homogeneous)35
b(quadratic)e(form)g(on)1645 742 y(\026)1623 767 y Fr(P)47
b Fs(is)56 947 y Fq(\000)22 b Fr(z)205 906 y Fo(26)201
971 y Fn(i)290 947 y Fr(z)340 906 y Fo(13)336 971 y Fn(j)448
947 y Fq(\000)g Fr(z)597 906 y Fo(26)593 971 y Fn(i)682
947 y Fr(z)732 906 y Fo(15)728 971 y Fn(j)840 947 y Fs(+)g
Fr(z)989 906 y Fo(31)985 971 y Fn(j)1074 947 y Fr(z)1124
906 y Fo(53)1120 971 y Fn(j)1232 947 y Fs(+)g Fr(z)1381
906 y Fo(35)1377 971 y Fn(j)1466 947 y Fr(z)1516 906
y Fo(15)1512 971 y Fn(j)1624 947 y Fs(+)g Fr(z)1773 906
y Fo(15)1769 971 y Fn(j)1858 947 y Fr(z)1908 906 y Fo(13)1904
971 y Fn(j)2016 947 y Fs(+)g(\()p Fr(z)2204 906 y Fo(13)2200
971 y Fn(j)2289 947 y Fs(\))2328 906 y Fo(2)2395 947
y Fs(+)g(\()p Fr(z)2583 906 y Fo(15)2579 971 y Fn(j)2668
947 y Fs(\))2707 906 y Fo(2)2774 947 y Fs(+)g(\()p Fr(z)2962
906 y Fo(35)2958 971 y Fn(j)3047 947 y Fs(\))3086 906
y Fo(2)3153 947 y Fs(+)g(\()p Fr(z)3341 906 y Fo(26)3337
971 y Fn(i)3426 947 y Fs(\))3465 906 y Fo(2)56 1113 y
Fs(+)g(\()p Fr(a)247 1128 y Fo(3)314 1113 y Fs(+)g Fr(a)466
1128 y Fo(5)533 1113 y Fq(\000)g Fr(a)685 1128 y Fo(2)752
1113 y Fq(\000)g Fr(a)904 1128 y Fo(6)949 1113 y Fs(\))p
Fr(z)1038 1071 y Fo(62)1034 1137 y Fn(i)1145 1113 y Fs(+)g(\()p
Fr(a)1336 1128 y Fo(2)1403 1113 y Fq(\000)g Fr(a)1555
1128 y Fo(1)1622 1113 y Fq(\000)g Fr(a)1774 1128 y Fo(3)1819
1113 y Fs(\))p Fr(z)1908 1071 y Fo(31)1904 1137 y Fn(j)2015
1113 y Fs(+)g(\()p Fr(a)2206 1128 y Fo(2)2273 1113 y
Fs(+)g Fr(a)2425 1128 y Fo(4)2492 1113 y Fq(\000)g Fr(a)2644
1128 y Fo(1)2711 1113 y Fq(\000)g Fs(2)p Fr(a)2913 1128
y Fo(3)2980 1113 y Fq(\000)g Fr(a)3132 1128 y Fo(5)3177
1113 y Fs(\))p Fr(z)3266 1071 y Fo(51)3262 1137 y Fn(j)56
1278 y Fs(+)g(\()p Fr(a)247 1293 y Fo(4)314 1278 y Fq(\000)g
Fr(a)466 1293 y Fo(3)533 1278 y Fq(\000)g Fr(a)685 1293
y Fo(5)730 1278 y Fs(\))p Fr(z)819 1237 y Fo(53)815 1303
y Fn(j)903 1278 y Fr(:)120 1458 y Fs(There)27 b(are)g(again)g(5)g
(indep)s(enden)m(t)i(v)-6 b(ariables:)41 b(the)27 b(8)g(v)-6
b(ariables)26 b(ab)s(o)m(v)m(e)h(satisfy)g(the)g(linear)0
1578 y(relations:)496 1757 y Fr(z)546 1716 y Fo(13)542
1782 y Fn(j)653 1757 y Fs(+)22 b Fr(z)802 1716 y Fo(53)798
1782 y Fn(j)915 1757 y Fs(=)28 b Fr(z)1070 1716 y Fo(31)1066
1782 y Fn(j)1178 1757 y Fs(+)22 b Fr(z)1327 1716 y Fo(35)1323
1782 y Fn(j)1412 1757 y Fr(;)116 b(z)1606 1716 y Fo(15)1602
1782 y Fn(j)1714 1757 y Fs(+)22 b Fr(z)1863 1716 y Fo(13)1859
1782 y Fn(j)1976 1757 y Fs(=)28 b Fr(z)2131 1716 y Fo(51)2127
1782 y Fn(j)2238 1757 y Fs(+)23 b Fr(z)2388 1716 y Fo(53)2384
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%%Page: 13 13
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3450 y Fs(under)25 b(the)f(ob)m(vious)f(map)3133 3425
y(~)3111 3450 y Fr(F)16 b Fq(\002)3268 3465 y Fn(E)3360
3425 y Fs(~)3338 3450 y Fr(F)42 b Fq(!)0 3570 y Fr(F)36
b Fq(\002)23 b Fr(F)14 b Fs(.)120 3689 y(This)33 b(de\014nes)i(the)f
(required)f(partition)g(of)1788 3664 y(~)1765 3689 y
Fr(F)j Fq(\002)1942 3704 y Fn(E)2055 3664 y Fs(~)2032
3689 y Fr(F)14 b Fs(.)120 3810 y(F)-8 b(or)32 b(example,)h(the)h
(diagonal)1309 3785 y(~)1286 3810 y Fr(F)42 b Fq(\032)1519
3785 y Fs(~)1497 3810 y Fr(F)36 b Fq(\002)1674 3825 y
Fn(E)1786 3785 y Fs(~)1764 3810 y Fr(F)47 b Fs(is)33
b(precisely)h(\()2444 3785 y(~)2422 3810 y Fr(F)i Fq(\002)2599
3825 y Fn(E)2711 3785 y Fs(~)2689 3810 y Fr(F)14 b Fs(\))2806
3825 y Fn(z)2844 3835 y Fd(a)2923 3810 y Fs(\(see)34
b(no.5\).)120 3930 y(No)m(w)e(the)i(v)-6 b(ariet)m(y)33
b(\()p Fr(F)i Fq(\002)23 b Fr(F)14 b Fs(\))1203 3945
y Fn(z)1282 3930 y Fs(is)33 b(a)g(connected)i(homogeneous)f(space)h(of)
e(dimension)1025 4082 y Ff(X)1083 4294 y Fn(i)1265 4082
y Ff(X)1185 4300 y Fn(r)n(;p)p Fp(2)p Fn(Z)5 b Fo(\()p
Fn(i)p Fo(\))1505 4176 y Fr(a)1558 4191 y Fn(p)1603 4176
y Fr(a)1656 4191 y Fn(r)1722 4176 y Fq(\000)1822 4082
y Ff(X)1880 4294 y Fn(i)2022 4082 y Ff(X)1983 4278 y
Fn(p;q)s(;r)n(;s)2023 4349 y(r)r Fp(\024)p Fn(p)2025
4421 y(s)p Fp(\024)p Fn(q)2223 4176 y Fr(z)2273 4128
y Fn(pq)2269 4204 y(i)2358 4176 y Fr(z)2408 4135 y Fn(r)r(s)2404
4201 y(i)2491 4176 y Fr(;)0 4636 y Fs(\(compare)34 b([BLM,)e(2.2].\))
120 4755 y(W)-8 b(e)47 b(\014x)g(\()p Fr(\036;)17 b( )t
Fs(\))50 b Fq(2)i Fs(\()p Fr(F)45 b Fq(\002)32 b Fr(F)14
b Fs(\))1253 4770 y Fn(z)1346 4755 y Fs(and)48 b(c)m(ho)s(ose)g
Fr(U)1963 4719 y Fn(r)r(s)1952 4781 y(i)2092 4755 y Fs(as)f(ab)s(o)m(v)
m(e.)87 b(Let)47 b Fr(Y)70 b Fs(b)s(e)47 b(the)h(v)-6
b(ariet)m(y)0 4883 y(consisting)47 b(of)f(all)f Fr(x)50
b Fq(2)g Fr(E)h Fs(suc)m(h)d(that)e(\()p Fr(x;)17 b(\036)p
Fs(\))48 b Fq(2)1991 4858 y Fs(~)1969 4883 y Fr(F)14
b(;)j Fs(\()p Fr(x;)g( )t Fs(\))47 b Fq(2)2526 4858 y
Fs(~)2504 4883 y Fr(F)13 b Fs(.)84 b(The)46 b(condition)h(that)0
5003 y Fr(x)28 b Fs(=)g(\()p Fr(x)286 5018 y Fn(h)337
5003 y Fs(\))33 b(is)g(in)g Fr(Y)56 b Fs(is)33 b(that)1221
5242 y Fr(x)1278 5257 y Fn(h)1330 5242 y Fs(\()p Fr(U)1448
5194 y Fn(pq)1437 5272 y(h)1484 5252 y Fm(0)1533 5242
y Fs(\))27 b Fq(\032)h(\010)1781 5265 y Fn(r)n(;s)p Fp(2)p
Fn(Z)5 b Fo(\()p Fn(h)2069 5235 y Fm(0)o(0)2117 5265
y Fo(\))1894 5341 y Fn(r)r Fp(\024)p Fn(p)1896 5412 y(s)p
Fp(\024)p Fn(q)2153 5242 y Fr(U)2232 5201 y Fn(r)r(s)2221
5266 y(h)2268 5246 y Fm(00)p eop end
%%Page: 16 16
TeXDict begin 16 15 bop 0 50 a Fi(16)1419 b(G.)37 b(LUSZTIG)0
289 y Fs(for)c(all)g Fr(h)28 b Fq(2)g Fs(\012)33 b(and)h(all)e
Fr(p;)17 b(q)31 b Fq(2)d Fr(Z)7 b Fs(\()p Fr(h)1342 253
y Fp(0)1371 289 y Fs(\).)120 408 y(Th)m(us,)34 b Fr(Y)55
b Fs(is)33 b(a)g(v)m(ector)g(space)h(of)g(dimension)945
662 y(dim)16 b Fr(Y)50 b Fs(=)1340 567 y Ff(X)1389 782
y Fn(h)1612 567 y Ff(X)1508 791 y Fn(p;q)s Fp(2)p Fn(Z)5
b Fo(\()p Fn(h)1804 761 y Fm(0)1829 791 y Fo(\))1501
876 y Fn(r)n(;s)p Fp(2)p Fn(Z)g Fo(\()p Fn(h)1789 846
y Fm(0)n(0)1836 876 y Fo(\))1613 952 y Fn(r)r Fp(\024)p
Fn(p)1615 1023 y(s)p Fp(\024)p Fn(q)1884 662 y Fs(dim)17
b Fr(U)2146 614 y Fn(pq)2135 692 y(h)2182 672 y Fm(0)2247
662 y Fs(dim)g Fr(U)2509 621 y Fn(r)r(s)2498 687 y(h)2545
667 y Fm(00)120 1268 y Fs(It)32 b(follo)m(ws)i(that)e(\()832
1243 y(~)809 1268 y Fr(F)k Fq(\002)986 1283 y Fn(E)1099
1243 y Fs(~)1076 1268 y Fr(F)14 b Fs(\))1193 1283 y Fn(z)1272
1268 y Fs(is)33 b(irreducible,)h(of)f(dimension)576 1507
y Fq(\000)670 1413 y Ff(X)728 1625 y Fn(i)870 1413 y
Ff(X)830 1609 y Fn(p;q)s(;r)n(;s)871 1680 y(r)r Fp(\024)p
Fn(p)873 1752 y(s)p Fp(\024)p Fn(q)1070 1507 y Fr(z)1120
1459 y Fn(pq)1116 1535 y(i)1206 1507 y Fr(z)1256 1466
y Fn(r)r(s)1252 1532 y(i)1361 1507 y Fs(+)1460 1413 y
Ff(X)1509 1627 y Fn(h)1660 1413 y Ff(X)1621 1609 y Fn(p;q)s
Fo(;)p Fn(r)n(;s)1661 1680 y(r)r Fp(\024)p Fn(p)1663
1752 y(s)p Fp(\024)p Fn(q)1860 1507 y Fr(z)1910 1459
y Fn(pq)1906 1537 y(h)1953 1517 y Fm(0)1996 1507 y Fr(z)2046
1466 y Fn(r)r(s)2042 1532 y(h)2089 1512 y Fm(00)2165
1507 y Fs(+)2264 1413 y Ff(X)2322 1625 y Fn(i)2504 1413
y Ff(X)2425 1631 y Fn(r)n(;p)p Fp(2)p Fn(Z)5 b Fo(\()p
Fn(i)p Fo(\))2744 1507 y Fr(a)2797 1522 y Fn(p)2843 1507
y Fr(a)2896 1522 y Fn(r)2940 1507 y Fr(:)120 1947 y Fs(In)33
b(particular,)754 1921 y(~)732 1947 y Fr(F)837 1920 y
Fq(\030)837 1952 y Fs(=)942 1947 y(\()1004 1921 y(~)981
1947 y Fr(F)j Fq(\002)1158 1962 y Fn(E)1270 1921 y Fs(~)1248
1947 y Fr(F)14 b Fs(\))1365 1962 y Fn(z)1403 1972 y Fd(a)1483
1947 y Fs(is)33 b(irreducible,)h(of)f(dimension)570 2186
y Fq(\000)664 2091 y Ff(X)722 2303 y Fn(i)906 2091 y
Ff(X)825 2309 y Fn(p;r)r Fp(2)p Fn(Z)5 b Fo(\()p Fn(i)p
Fo(\))907 2385 y Fn(r)r Fp(\024)p Fn(p)1149 2186 y Fr(a)1202
2201 y Fn(p)1247 2186 y Fr(a)1300 2201 y Fn(r)1366 2186
y Fs(+)1466 2091 y Ff(X)1514 2306 y Fn(h)1709 2091 y
Ff(X)1636 2315 y Fn(p)p Fp(2)p Fn(Z)g Fo(\()p Fn(h)1868
2285 y Fm(0)1895 2315 y Fo(\))1626 2400 y Fn(r)r Fp(2)p
Fn(Z)g Fo(\()p Fn(h)1856 2370 y Fm(00)1905 2400 y Fo(\))1710
2476 y Fn(r)r Fp(\024)p Fn(p)1953 2186 y Fr(a)2006 2201
y Fn(p)2051 2186 y Fr(a)2104 2201 y Fn(r)2170 2186 y
Fs(+)2270 2091 y Ff(X)2328 2303 y Fn(i)2510 2091 y Ff(X)2430
2309 y Fn(r)n(;p)p Fp(2)p Fn(Z)g Fo(\()p Fn(i)p Fo(\))2750
2186 y Fr(a)2803 2201 y Fn(p)2849 2186 y Fr(a)2902 2201
y Fn(r)2945 2186 y Fr(:)120 2648 y Fs(Substracting)34
b(the)f(previous)h(t)m(w)m(o)f(expressions,)h(w)m(e)g(obtain)1049
2889 y(dim\()1276 2863 y(~)1254 2889 y Fr(F)14 b Fs(\))22
b Fq(\000)g Fs(dim\()1719 2863 y(~)1697 2889 y Fr(F)36
b Fq(\002)1874 2904 y Fn(E)1986 2863 y Fs(~)1964 2889
y Fr(F)14 b Fs(\))2081 2904 y Fn(z)2154 2889 y Fs(=)29
b Fr(Q)p Fs(\()p Fr(z)t Fs(\))p Fr(:)0 3128 y Fs(\(See)39
b(5\(a\).\))56 b(This)39 b(implies)f(directly)f(statemen)m(ts)i(\(a\))e
(and)h(\(b\))g(ab)s(o)m(v)m(e.)58 b(The)39 b(Theorem)f(is)0
3247 y(pro)m(v)m(ed.)1481 3486 y Ft(References)0 3646
y Fi([BBD])-82 b(A.)28 b(A.)g(Beilinson,)f(J.)h(Bernstein)f(and)i(P)-7
b(.)27 b(Deligne,)f Fh(F)-7 b(aisc)l(e)l(aux)31 b(p)l(ervers)p
Fi(,)d(Ast)n(\023)-40 b(erisque)28 b Fc(100)g Fi(\(1982\).)0
3745 y([BLM])-88 b(A.)27 b(A)g(Beilinson,)f(G.)h(Lusztig)g(and)h(R.)f
(MacPherson,)f Fh(A)k(ge)l(ometric)h(setting)h(for)d(the)i(quantum)f
(defor-)151 3845 y(mation)g(of)h Fb(GL)666 3855 y Fa(n)716
3845 y Fi(,)d(Duk)n(e)f(Math.)h(J.)g Fc(61)g Fi(\(1990\),)h(655-677.)0
3945 y([K])37 b(M.)23 b(Kashiw)n(ara,)i Fh(On)h(crystal)h(b)l(ases)g
(of)g(the)g Fb(q)s Fh(-analo)l(gue)f(of)g(the)i(universal)f(enveloping)
h(algebr)l(as)p Fi(,)d(Duk)n(e)151 4044 y(Math.)i(J.)h
Fc(2)g Fi(\(1991\),)h(465-516.)0 4144 y([L1])8 b(G.)40
b(Lusztig,)j Fh(Gr)l(e)l(en)g(p)l(olynomials)d(and)i(singularities)h
(of)g(unip)l(otent)f(classes)p Fi(,)i(Adv.)c(in)g(Math.)k
Fc(42)151 4244 y Fi(\(1981\),)29 b(169-178.)0 4343 y([L2])p
151 4343 255 4 v 276 w(,)i Fh(Quivers,)j(p)l(erverse)g(she)l(aves)f
(and)f(quantize)l(d)i(enveloping)g(algebr)l(as)p Fi(,)d(J.)f(Amer.)g
(Math.)g(So)r(c.)151 4443 y Fc(4)e Fi(\(1991\),)h(365-421.)0
4542 y([L3])p 151 4542 V 276 w(,)e Fh(Intr)l(o)l(duction)k(to)g
(quantize)l(d)g(enveloping)h(algebr)l(as)c Fi(\(1990\),)h(preprin)n(t.)
0 4642 y([M])c(I.)c(G.)h(Macdonald,)g Fh(Symmetric)j(functions)h(and)e
(Hal)t(l)h(p)l(olynomials)p Fi(,)20 b(Clarendon)i(Press,)g(Oxford,)g
(1979.)0 4742 y([R])41 b(C.)27 b(M.)h(Ringel,)f Fh(Hal)t(l)k(algebr)l
(as)f(and)h(quantum)g(gr)l(oups)p Fi(,)c(In)n(v)n(en)n(t.)f(Math.)i
Fc(101)g Fi(\(1990\),)h(583-592.)p eop end
%%Trailer
userdict /end-hook known{end-hook}if
%%EOF