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Finite-Dimensional Irreducible Modules of the Universal Askey–Wilson Algebra

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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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Authors and Affiliations

  1. Einstein Institute of Mathematics, Hebrew University, Jerusalem, 91904, Israel

    Hau-Wen Huang

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Correspondence to Hau-Wen Huang.

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Communicated by Y. Kawahigashi

The research was supported by the National Center for Theoretical Sciences of Taiwan and the Council for Higher Education of Israel.

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Huang, HW. Finite-Dimensional Irreducible Modules of the Universal Askey–Wilson Algebra. Commun. Math. Phys. 340, 959–984 (2015). https://doi.org/10.1007/s00220-015-2467-9

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