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Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra

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arxiv 1806.02656 v2 pith:KA3M6FKH submitted 2018-06-01 math.QA

Pascal Baseilhac , Xavier Martin , Luc Vinet , Alexei Zhedanov This is my paper · ORCID
classification math.QA
keywords algebraaskey-wilsonlittlepolynomialsmathfrakq-jacobiarisebasis
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abstract

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey-Wilson algebra generated by twisted primitive elements of $\mathfrak U_q(sl(2))$. The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey-Wilson algebra into $\mathfrak U_q(sl(2))$.

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  1. 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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