David Nadler : Character sheaves for loop groups

Posted by Mihnea Popa , part of the Algebraic Geometry Seminar.

At

Oct. 19, 2011, 4 p.m.

In

SEO 427

Abstract

I'll discuss joint work with D. Ben-Zvi (Texas) devoted to characters of categorical loop group representations. From one perspective, such characters should be adjoint-equivariant sheaves on the loop group itself. Unfortunately, the adjoint-quotient of a loop group is a fearsome infinite (both positive and negative) dimensional stack. Fortunately, gauge theory provides another perspective in which such characters should be sheaves on the moduli of bundles on an elliptic curve. This leads to many interesting connections with other parts of representation theory, and in particular a Langlands dual spectral description in terms of commuting varieties.