Elsevier

Advances in Mathematics

Volume 220, Issue 6, 1 April 2009, Pages 1657-1688
Advances in Mathematics

The BRST reduction of the chiral Hecke algebra

https://doi.org/10.1016/j.aim.2008.10.015Get rights and content
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Abstract

We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a gˆκ-module that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its untwisted BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds between the regular cohomology and the Iwahori orbits on the affine flag manifold. As an application of the above, we describe the BRST reduction of the chiral Hecke algebra as a vertex super algebra.

MSC

17B99

Keywords

Chiral Hecke algebra
Affine Kac–Moody Lie algebra
Semi-infinite cohomology
D-module

Cited by (0)

The main results in this paper are part of the author's doctoral dissertation, written at the University of Chicago under the supervision of Alexander Beilinson. The author wishes to thank Professor Beilinson for many illuminating discussions over the years as well as careful readings of the drafts of this paper. Additional work on this text was carried out at UC Davis, MPI (Bonn), IHES, and the University of Waterloo. Many thanks are also due to Roman Bezrukavnikov for helpful discussions.