Representations of Askey--Wilson algebra

TL;DR

This paper classifies finite-dimensional representations of the Askey--Wilson algebra when q is not a root of unity, focusing on those with diagonalizable generators, advancing understanding of its algebraic structure.

Contribution

It provides a complete classification of certain finite-dimensional representations of the Askey--Wilson algebra under specific diagonalizability conditions.

Findings

Classified all representations with diagonalizable generators

Identified conditions ensuring diagonalizability

Enhanced understanding of Askey--Wilson algebra structure

Abstract

We deal with the classification problem of finite-dimensional representations of so called Askey--Wilson algebra in the case when $q$ is not a root of unity. We classify all representations satisfying certain property, which ensures diagonalizability of one of the generating elements.