The Jordanian deformation of su(2) and Clebsch-Gordan coefficients

Abstract

Representation theory for the Jordanian quantum algebra U=U_h(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of U on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the generators of U have a simple action. Using this basis, a general formula is obtained for the Clebsch-Gordan coefficients of U. It is shown that the Clebsch-Gordan matrix is essentially the product of a triangular matrix with an su(2) Clebsch-Gordan matrix. Using this fact, some remarkable properties of these Clebsch-Gordan coefficients are derived.