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

2012/10/05 by Hau-Wen Huang, Huang, Hau-wen · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1210.1740

openalex publication_date 2012/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \triangle_q of the Askey-Wilson algebras was recently studied. In this paper, we consider a family of infinite-dimensional \triangle_q-modules. By the universal property of these \triangle_q-modules, we classify the finite-dimensional irreducible \triangle_q-modules when q is not a root of unity.

Citations

• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

Cited by

• The Askey--Wilson algebras, the Lie algebra \mathfrakso₃, and their fermionic realizations

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