Rigid dualizing complexes of affine Hecke algebras

TL;DR

This paper determines the rigid dualizing complex of affine Hecke algebras associated with root systems and explores their Frobenius properties and automorphisms, revealing structural insights into these algebraic objects.

Contribution

It identifies the rigid dualizing complex of the generic affine Hecke algebra and establishes Frobenius properties and explicit Nakayama automorphisms under certain conditions.

Findings

The rigid dualizing complex of the affine Hecke algebra is explicitly identified.

Affine Hecke algebras are Frobenius over their centers under certain conditions.

Explicit involutions serve as Nakayama automorphisms for these algebras.

Abstract

We identify the rigid dualizing complex of the (generic) affine Hecke algebra $H_q$ attached to a reduced root system and deduce some structural properties as a consequence. For example, we show that the classical Hecke algebra $H_{q^\pm}$ as well as $H_q/q$ are, under a certain condition on the root system, Frobenius over their centers with Nakayama automorphism given by an explicit involution.