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

11 pages

References in corpus (2)

• Bispectrality of the Complementary Bannai-Ito Polynomials
• An embedding of the universal Askey-Wilson algebra into $U_q({\mathfrak{sl}}_2)\otimes U_q({\mathfrak{sl}}_2)\otimes U_q({\mathfrak{sl}}_2)$

Cited by in corpus (5)

• The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
• Finite-dimensional irreducible modules of the Bannai--Ito algebra at characteristic zero
• Bargmann and Barut-Girardello models for the Racah algebra
• Superspace realizations of the Bannai-Ito algebra
• Convolution identities for Dunkl orthogonal polynomials from the $\mathfrak{osp}(1|2)$ Lie superalgebra