Little and big q-Jacobi polynomials and the Askey–Wilson algebra

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 Uq(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 Uq(sl(2)).
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Pascal Baseilhac, Xavier Martin, Luc Vinet, Alexei Zhedanov. Little and big q-Jacobi polynomials and the Askey–Wilson algebra. Ramanujan Journal, Springer Verlag, 2019, ⟨10.1007/s11139-018-0080-1⟩. ⟨hal-02152836⟩

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