An embedding of the Bannai-Ito algebra in $U(osp(1,2))$ and −1 polynomials

Luc Vinet (1) , Alexei Zhedanov , Vincent Genest

1 CRM - Centre de Recherches Mathématiques [Montréal]

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

Keywords: Askey-Wilson algebra; Special functions

Domains: Mathematics [math]; Mathematical Physics [math-ph]; Mathematics [math]; Representation Theory [math.RT]

Luc Vinet, Alexei Zhedanov, Vincent Genest. An embedding of the Bannai-Ito algebra in $U(osp(1,2))$ and −1 polynomials. 2017. ⟨cea-01529434⟩