Linear Koszul duality and Fourier transform for convolution algebras
Representation Theory
2015-09-15 v3
Abstract
In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-homology defined in a previous paper and the Fourier transform isomorphism for convolution algebras in Borel-Moore homology are related by the Chern character. So, Koszul duality appears as a categorical upgrade of Fourier transform of constructible sheaves. This result explains the connection between the categorification of the Iwahori-Matsumoto involution for graded affine Hecke algebras (due to Evens and the first author) and for usual affine Hecke algebras (obtained in a previous paper).
Cite
@article{arxiv.1401.7186,
title = {Linear Koszul duality and Fourier transform for convolution algebras},
author = {Ivan Mirkovic and Simon Riche},
journal= {arXiv preprint arXiv:1401.7186},
year = {2015}
}
Comments
v1: 29 pages; v2: 41 pages, many details added; v3: 42 pages, minor modifications (final version, to appear in Doc. Math.)