Abstract:
We consider the compact quantum group Uq(2)for qEC\{0} with |q|≠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 Uq(2). Then, we compute the Clebsch–Gordan coefficients in terms of the q-hypergeometric series 3Φ2. When q is real, the Clebsch-Gordan coefficients are real and its expression can be written in terms of the q-Hahn polynomial.