An embedding of the Bannai–Ito algebra in U(osp(1,2)) and −1 polynomials

Abstract : An embedding of the Bannai–Ito algebra in the universal enveloping algebra of osp(1,2) is provided. A connection with the characterization of the little −1 Jacobi polynomials is found in the holomorphic realization of osp(1,2). An integral expression for the Bannai–Ito polynomials is derived as a corollary.
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Pascal Baseilhac, Vincent Genest, Luc Vinet, Alexei Zhedanov. An embedding of the Bannai–Ito algebra in U(osp(1,2)) and −1 polynomials. Letters in Mathematical Physics, Springer Verlag, 2018, 108 (7), pp.1623-1634. ⟨10.1007/s11005-017-1041-0⟩. ⟨hal-02154124⟩

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