Joint seminar: Combinatorics and Lie Groups
Totally non negative and oscillatory elements in semi-simple groups
refreshments at 3:45pm
A matrix is totally positive (resp. totally nonnegative) if
all its minors are positive (resp. nonnegative) real numbers. The
first systematic study of these matrices was undertaken in the 1930s
by F.R. Gantmacher and M.G. Krein. More recently, G. Lusztig
discovered a surprising connection between total positivity and
canonical bases for quantum groups, and extended the subject by
defining totally positive and totally nonnegative elements for any
semisimple group. We shall discuss some classical results about total
positivity, and how to extend them to arbitrary semisimple groups.
Most of the new results to be discussed were obtained jointly with
Speaker's Contact Info: andrei(at-sign)neu.edu
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