# 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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https://hal-cea.archives-ouvertes.fr/cea-01529434
Contributor : Pascal Baseilhac <>
Submitted on : Tuesday, May 30, 2017 - 6:14:55 PM
Last modification on : Tuesday, October 6, 2020 - 9:48:13 AM

### Identifiers

• HAL Id : cea-01529434, version 1
• ARXIV : 1705.09737

### Citation

Luc Vinet, Alexei Zhedanov, Vincent Genest. An embedding of the Bannai-Ito algebra in $U(osp(1,2))$ and −1 polynomials. 2017. ⟨cea-01529434⟩

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