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

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