Representation properties, Racah sum rule, and Biedenharn–Elliott identity for Uq(osp(1|2))

Abstract

It is shown that the universal R matrix in the tensor product of two irreducible representation spaces of the quantum superalgebra Uq(osp(1|2)) can be expressed by Clebsch–Gordan coefficients. The Racah sum rule satisfied by Uq(osp(1|2)) Racah coefficients and 6−j symbols is derived from the properties of the universal R matrix in the tensor product of three representation spaces. Considering the tensor product of four irreducible representations, it is shown that Biedenharn–Elliott identity holds for Uq(osp(1|2)) Racah coefficients and 6−j symbols. A recursion relation for Uq(osp(1|2)) 6−j symbols is derived from the Biedenharn–Elliott identity.