Iwahori-Matsumoto involution and linear Koszul Duality

TL;DR

This paper explores the geometric realization of the Iwahori-Matsumoto involution in affine Hecke algebras using linear Koszul duality, and demonstrates its compatibility with convolution in a broad algebraic context.

Contribution

It introduces a geometric approach to understanding the Iwahori-Matsumoto involution via linear Koszul duality and establishes its compatibility with convolution operations.

Findings

Linear Koszul duality provides a geometric realization of the Iwahori-Matsumoto involution.

The duality is shown to be compatible with convolution in a general algebraic setting.

The work extends previous algebraic dualities to a geometric framework.

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.