Representations of Rank Two Affine Hecke Algebras at Roots of Unity

TL;DR

This paper provides a complete description of the representations of rank two affine Hecke algebras at roots of unity, focusing on cases where q is a small-order root of unity, using elementary methods.

Contribution

It offers a comprehensive classification of these representations for all q, especially at roots of unity of small order, using elementary techniques.

Findings

Complete classification of rank two affine Hecke algebra representations at roots of unity.

Explicit descriptions for small-order roots of unity.

Methodological advancement with elementary techniques.

Abstract

In this paper, we will fully describe the representations of the crystallographic rank two affine Hecke algebras using elementary methods, for all possible values of q. The focus is on the case when q is a root of unity of small order.