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arXiv · 1806.02656

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

Pascal Baseilhac·Xavier Martin·Luc Vinet·Alexei Zhedanov
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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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Pascal Baseilhac, Xavier Martin, Luc Vinet, Alexei Zhedanov. 2018-06-01. Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra. https://arxiv.org/abs/1806.02656

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