An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials

Pascal Baseilhac; Vincent X. Genest; Luc Vinet; Alexei Zhedanov

doi:10.1007/s11005-017-1041-0

An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials

Mathematical Physics 2018-03-14 v1 math.MP

Authors: Pascal Baseilhac , Vincent X. Genest , Luc Vinet , Alexei Zhedanov

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Abstract

An embedding of the Bannai-Ito algebra in the universal enveloping algebra of $\mathfrak{osp}(1,2)$ is provided. A connection with the characterization of the little $-1$ Jacobi polynomials is found in the holomorphic realization of $\mathfrak{osp}(1,2)$ . An integral expression for the Bannai-Ito polynomials is derived as a corollary.

Keywords

Bannai-Ito algebra universal enveloping algebra osp(1,2) holomorphic realization little -1 Jacobi polynomials Bannai-Ito polynomials integral expression

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@article{arxiv.1705.09737,
  title  = {An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials},
  author = {Pascal Baseilhac and Vincent X. Genest and Luc Vinet and Alexei Zhedanov},
  journal= {arXiv preprint arXiv:1705.09737},
  year   = {2018}
}

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11 pages

An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials

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