Loop Spaces and Langlands Parameters

Details Loop Spaces and Langlands Parameters Loop Spaces and Langlands Parameters

2007-06-03

arxiv.org/abs/0706.0322v1

Mathematics

Representation Theory

Preliminary version. Comments welcome!

Scientific paper

We apply the technique of S^1-equivariant localization to sheaves on loop spaces in derived algebraic geometry, and obtain a fundamental link between two families of categories at the heart of geometric representation theory. Namely, we categorify the well known relationship between free loop spaces, cyclic homology and de Rham cohomology to recover the category of D-modules on a smooth stack X as a localization of the category of S^1-equivariant coherent sheaves on its loop space LX. The main observation is that this procedure connects categories of equivariant D-modules on flag varieties with categories of equivariant coherent sheaves on the Steinberg variety and its relatives. This provides a direct connection between the geometry of finite and affine Hecke algebras and braid groups, and a uniform geometric construction of all of the categorical parameters for representations of real and complex reductive groups. This paper forms the first step in a project to apply the geometric Langlands program to the complex and real local Langlands programs, which we describe.

Affiliated with

Also associated with

No associations

Rating

Loop Spaces and Langlands Parameters does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Loop Spaces and Langlands Parameters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Loop Spaces and Langlands Parameters will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-689122