Decomposition of tensor product representations of the unitary matrix quantum group SU_q(2)

Representations of SU_q(2) are labeled by a phase playing the role of a Casimir operator. The coproduct SU_q(2) is used to form direct product representations which can be reduced to irreducible ones. Direct product of two representations with given phases can be reduced to a representation with any given phase. Coefficients necessary for this procedure are calculated. The calculation can also be performed in the Fourier transformed space which replaces the phase by an integer.