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

## TL;DR

This paper embeds the Bannai-Ito algebra into the universal enveloping algebra of rak{osp}(1,2), linking it to little  Jacobi polynomials and deriving an integral expression for Bannai-Ito polynomials.

## Contribution

It introduces a novel embedding of the Bannai-Ito algebra into rak{osp}(1,2) and connects it to the characterization of little  Jacobi polynomials.

## Key findings

- Established an embedding of Bannai-Ito algebra in rak{osp}(1,2)
- Connected Bannai-Ito algebra to little  Jacobi polynomials
- Derived an integral expression for Bannai-Ito polynomials

## 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.