2011-04-22

Green functions via hyperbolic localization

Pramod Achar, Louisiana State University

By the mid-1980's, work of Lusztig, Shoji, and others had shown how to understand the representation theory of finite groups of Lie type using the geometry of algebraic groups. A key piece of this theory is an algorithm for computing certain class functions (Green functions), related to perverse sheaves on the nilpotent cone. I will explain how Braden's hyperbolic localization functor can be used to turn these "difficult" perverse sheaves into "easy" modules over the cohomology of the flag variety, and how one can get a new proof of the Lusztig-Shoji algorithm in the process.