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

Pascal Baseilhac; Vincent Genest; Luc Vinet; Alexei Zhedanov

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 Massachussets Institute of Technology

3 CRM - Centre de Recherches Mathématiques [Montréal]

4 Renmin University of China, Beijing

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

Document type :

Journal articles

Domain :

Mathematics [math] / Mathematical Physics [math-ph]

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Last modification on : Friday, June 14, 2019 - 2:06:07 AM

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

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