Generating functions for the osp(1|2) Clebsch-Gordan coefficients

Abstract

Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generating functions are obtained using two different approaches respectively based on the coherent-state representation and the position representation of osp(1j2).

21 pages

References in corpus (4)

• Bispectrality of the Complementary Bannai-Ito Polynomials
• A Laplace-Dunkl equation on $S^2$ and the Bannai-Ito algebra
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)

Cited by in corpus (4)

• Ghost center and representations of the diagonal reduction algebra of $\mathfrak{osp}(1|2)$
• Superintegrability and the dual $-1$ Hahn algebra in superconformal quantum mechanics
• A Howe correspondence for the algebra of the $\mathfrak{osp}(1|2)$ Clebsch-Gordan coefficients
• Convolution identities for Dunkl orthogonal polynomials from the $\mathfrak{osp}(1|2)$ Lie superalgebra