Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra

New convolution identities for orthogonal polynomials belonging to the q = -1 analog of the Askey-scheme are obtained. Specialization of the Chihara polynomials will play a central role as the eigenfunctions of a special element of the Lie superalgebra osp(1|2) in the positive discrete series representation. Using the Clebsch-Gordan coefficients, a convolution identity for the specialized Chihara, the dual -1 Hahn and the Big -1 Jacobi polynomials are found. Using the Racah coefficients, a convolution identity for the Big -1 Jacobi and the Bannai-Ito polynomials is found. Finally, these results are applied to construct a bilinear generating function for the Big -1 Jacobi polynomials. Published under license by AIP Publishing.