Superspace realizations of the Bannai-Ito algebra

A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra $osp(1\mathrm{\mid }2)$ in terms of operators in one continuous and one Grassmanian variable. The basis vectors of the resulting Bannai-Ito algebra module involve Jacobi polynomials.