Algebraic Geometry Seminar
October 13, 2008
Title: Bases of Weyl group representations
Speakers: Peter Trapa (University of Utah)
Abstract: Let W denote the Weyl group of a complex semisimple algebraic group G. For instance, G could be n-by-n matrices of determinant one, and W could be the symmetric group on n letters. The theory of Springer, Joseph, and Kazhdan-Lusztig (among others) shows that the geometry of the projective varieties on which G acts miraculously leads to two distinguished bases of the irreducible representations of W. But there is no known effective means to relate these two bases. This talk will survey some of what is known, what isn't, what might be possible to prove, and why this is such an important problem (for instance in understanding representations of real and p-adic groups).
There will be an informal (free) seminar dinner after the talk. All are welcome.