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arXiv · 1705.09737

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
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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.

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Pascal Baseilhac, Vincent X. Genest, Luc Vinet, Alexei Zhedanov. 2017-05-26. An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials. https://doi.org/10.1007/s11005-017-1041-0

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