{TALK 
        {"September 29}
        {"Updown Robinson-Schensted correspondence through some
algebraic varieties}
        {"Itaru Terada}
        {"University of Tokyo}
        {"terada@ms.u-tokyo.ac.jp}
        {"
Steinberg showed that the Robinson-Schensted (R-S)
correspondence describes the relationship between two natural
labelings of the irreducible components of an algebraic variety,
sometimes called Steinberg's variety of triples.  We give a similar
interpretation, through some algebric varieties, of a variant of the
R-S correspondence, conceived by Stanley and Sundaram and modified by
Roby, which links the Brauer diagrams (also regarded as
fixed-point-free involutions) with updown tableaux (also called
oscillating tableaux).  The talk will include a correction to a former 
preprint by the speaker, as well as some recent developments.}
}