Title: Hecke algebras and involutions in Weyl groups

Speaker: Prof.George Lusztig (Massachusetts Institute of Technology)

Venue: Lecture Hall at BICMR, Peking University 北京国际数学研究中心报告厅（未名湖北岸82号甲乙丙，全斋西边）

Time: 2:30-3:30pm, June 1, 2012 (Friday)

Abstract:
This talk is based in part on joint work with D. Vogan. Let W be the Weyl group of a semisimple group. For two elements y,w of W a polynomial P_{y,w} was introduced by Kazhdan and me in the late 1970's. This polynomial enters in various character formulas in representation theory. When y,w are involutions it turns out that P_{y,w} splits canonically in the sum of two polynomials. The problem discussed in this talk is about how to compute the two parts of P_{y,w}. It is expected that these results are useful for the theory of unitary representations of complex semisimple groups.