On two geometric realizations of an affine Hecke algebra
Abstract
The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant functions on a semi-simple group over a local non-Archimedian field, and Grothendieck group of equivariant coherent sheaves on Steinberg variety of the Langlands dual group; this isomorphism due to Kazhdan--Lusztig and Ginzburg is a key step in the proof of tamely ramified local Langlands conjectures. The paper is a continuation of an earlier joint work with S. Arkhipov, it relies on technical material developed in a paper with Z. Yun.
Keywords
Cite
@article{arxiv.1209.0403,
title = {On two geometric realizations of an affine Hecke algebra},
author = {Roman Bezrukavnikov},
journal= {arXiv preprint arXiv:1209.0403},
year = {2021}
}
Comments
This version contains some post-publication corrections. The statements (including their numbering) have not changed except for Theorem 54 where a vector bundle has been replaced by its dual