CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
On Hecke Correspondences Rahbar Virk, CU
February 28, 2012 Math 350 2-3pm	Abstract I will report on my current (and ongoing) work on understanding Hecke correspondences on the flag variety. Hecke correspondences are generalizations of incidence correspondences on P^1 to general flag varieties. Since the pioneering work of Beilinson-Bernstein and Kashiwara-Brylinski (on D-modules), Goresky-Macpherson and Beilinson-Bernstein-Deligne's work (on intersection cohomology), and Lusztig-Kazhdan and Lusztig-Vogan's work (in representation theory), it has been understood that the representation theory of reductive groups is controlled by the geometry and combinatorics of these Hecke correspondences. I will present my own contributions to this study. Time permitting I will explain how this ties into efforts by Nat Thiem and myself to understand and generalize Lusztig's theory of character sheaves.

On Hecke Correspondences

Rahbar Virk, CU

February 28, 2012

Math 350

2-3pm

Abstract

I will report on my current (and ongoing) work on understanding Hecke correspondences on the flag variety.

Hecke correspondences are generalizations of incidence correspondences on P^1 to general flag varieties. Since the pioneering work of Beilinson-Bernstein and Kashiwara-Brylinski (on D-modules), Goresky-Macpherson and Beilinson-Bernstein-Deligne's work (on intersection cohomology), and Lusztig-Kazhdan and Lusztig-Vogan's work (in representation theory), it has been understood that the representation theory of reductive groups is controlled by the geometry and combinatorics of these Hecke correspondences. I will present my own contributions to this study.

Time permitting I will explain how this ties into efforts by Nat Thiem and myself to understand and generalize Lusztig's theory of character sheaves.