On Clebsch–Gordan coefficients and matrix elements of representations of the quantum algebra U q(su2)

Abstract

Clebsch–Gordan coefficients and matrix elements of irreducible representations of the quantum algebra Uq(su2) were considered in several papers. In particular, a few expressions for them were derived. An approach to Clebsch–Gordan coefficients and to matrix elements of representations of Uq(su2) on the base of the theory of basic hypergeometric functions is given. This approach allows one to obtain q-analogs of all well-known classical expressions for Clebsch–Gordan coefficients (most of them were absent). New symmetry relations, generating functions, and recurrence formulas for Clebsch–Gordan coefficients of Uq(su2) are obtained. Unlike other papers, Clebsch–Gordan coefficients and matrix elements are considered on the base of minimal theoretical constructions (in fact, without using the notion of a C* algebra and of a Hopf algebra).