Finite-dimensional irreducible modules of the universal Askey-Wilson algebra

Abstract

Since the introduction of Askey-Wilson algebras by Zhedanov in 1991, the classification of the finite-dimensional irreducible modules of Askey-Wilson algebras remains open. A universal analog ${△}_q$ of the Askey-Wilson algebras was recently studied. In this paper, we consider a family of infinite-dimensional ${△}_q$-modules. By the universal property of these ${△}_q$-modules, we classify the finite-dimensional irreducible ${△}_q$-modules when $q$ is not a root of unity.

22 pages

References in corpus (4)

• The Universal Askey-Wilson Algebra
• The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
• The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q({\mathfrak{sl}}_2)$
• Double Affine Hecke Algebras of Rank 1 and the $Z_3$-Symmetric Askey-Wilson Relations