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Hidden Symmetry of the Racah and Clebsch-Gordan Problems for the Quantum Algebra sl_q(2)

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arxiv hep-th/9304138 v1 pith:WYC4WCN3 submitted 1993-04-27 hep-th math.QA

Ya. I. Granovskii , A. S. Zhedanov This is my paper · ORCID
classification hep-thmath.QA
keywords algebrahiddensymmetryaskey-wilsonclebsch-gordanproblemsquantumracah
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abstract

The Askey-Wilson algebra $AW(3)$ with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra $sl_q(2)$. On the base of this hidden symmetry a simple method to calculate corresponding coefficients in terms of the Askey-Wilson polynomials is proposed.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$

    math.QA 2019-08 conditional novelty 7.0 of 10

    A new R-matrix formula defines the third Askey-Wilson generator as a conjugate of the Casimir element in U_q(sl(2))^{⊗3}, and the Askey-Wilson relations are derived from it.

  2. The rank two Jacobi algebra

    math-ph 2025-07 conditional novelty 6.0 of 10

    The bispectral operators of the two-variable Jacobi polynomials generate a rank two quadratic algebra with Racah and Jacobi subalgebras.

  3. Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra

    math.QA 2019-08 conditional novelty 6.0 of 10

    New commutation and q-commutation relations are proven for generators of the higher rank Askey-Wilson and q-Bannai-Ito algebras, extending the rank-one defining relations.

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