On the Clebsch-Gordan coefficients for the quantum group Uq(2)

We consider the compact quantum group U-q(2) for q is an element of C \ {0} with |q| not equal 1, and decompose the tensor product of two irreducible representations into irreducible components. The decomposition is realized in terms of a basis of homogeneous polynomials in four variables involving the matrix elements of the irreducible representations of U-q (2). Then, we compute the Clebsch-Gordan coefficients in terms of the q-hypergeometric series 3 phi(2). When q is real, the Clebsch-Gordan coefficients are real and its expression can be written in terms of the q-Hahn polynomial Q(n)(x; a, b, N|q(2)).