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

Pascal Baseilhac 1 Vincent Genest 2 Luc Vinet 3, * Alexei Zhedanov 4
* Corresponding author
1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Department of Mathematics [MIT]
3 CRM - Centre de Recherches Mathématiques [Montréal]
4 Department of Mathematics [Renmin]
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.
Keywords : Bannai–Ito algebra Quantum groups Orthogonal polynomials Integral representations
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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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