Linear Koszul duality and affine Hecke algebras

TL;DR

This paper demonstrates that a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras can be achieved through linear Koszul duality equivalence, linking algebraic and geometric perspectives.

Contribution

It establishes a new geometric interpretation of the Iwahori-Matsumoto involution via linear Koszul duality, connecting previous algebraic constructions with geometric methods.

Findings

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

The equivalence links algebraic structures of affine Hecke algebras with geometric duality.

The approach offers new insights into the representation theory of affine Hecke algebras.

Abstract

In this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.