Masoud Kamgarpour : Geometrization of principal series representations of GL(N)

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

Nov. 3, 2010, 2 p.m.

In

SEO 427

Abstract

In geometric representation theory, one often wishes to describe representations realized on spaces of invariant functions as trace functions of equivariant perverse sheaves. In the case of principal series representations of GL(N) over a local field F, i.e., representations obtained by parabolic induction from characters of the torus, there is a beautiful description of families of these representations realized on spaces of functions on GL(N) invariant under the translation action of the Iwahori subgroup, or a suitable smaller compact open subgroup, studied by Howe, Roche, Bushnell-Kutzko, and others. Based on conjectures of Drinfeld, I will define and describe perverse sheaves whose traces recover these families. This is joint work with Travis Schedler.