Iwahori-Matsumoto involution and linear Koszul Duality

Abstract

We use linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras studied in previous papers of the authors to give a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras. More generally we prove that linear Koszul duality is compatible with convolution in a general context related to convolution algebras.

v1: 29 pages, the present paper supersedes arXiv:0903.0678; v2: 26 pages, minor modifications; v3: 29 pages, final version, published in IMRN