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

We consider the compact quantum group U<inf>q</inf>(2) for q∈ C\ { 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 U<inf>q</inf>(2) . Then, we compute the Clebsch–Gordan coefficients in terms of the q-hypergeometric series <inf>3</inf>ϕ<inf>2</inf> . When q is real, the Clebsch–Gordan coefficients are real and its expression can be written in terms of the q-Hahn polynomial Q<inf>n</inf>(x; a, b, N| q²) .