Princeton University

 

Title:         Combinatorial proof of a character identity

 

Abstract:

 

The calculation of the (intersection) cohomology of a Siegel modular variety includes many difficult character identities (the fundamental lemma, for example). In this lecture, I want to concentrate on the character identity appearing at the infinite place, which involves, among other things, stable discrete series characters and appears to be related in some non-obvious way to an identity of Goresky, Kottwitz and MacPherson. Once we strip away all the Lie group complications, our identity becomes a very elementary statement and can proved directly using the geometry of the Coxeter complex of the symmetric group. The relation with the Goresky-Kottwitz-MacPherson identity also becomes clearer; in particular, neither identity follows from the other, but they should have a common generalization. This is joint work with Richard Ehrenborg and Margaret Readdy.