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arXiv · 1210.1740

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

Hau-wen Huang
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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.

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Hau-wen Huang. 2012-10-05. Finite-dimensional irreducible modules of the universal Askey-Wilson algebra. https://arxiv.org/abs/1210.1740

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