INTEGRATION OVER THE GROUP SPACE OF SUQ(2), CLEBSCH-GORDAN-COEFFICIENTS, AND RELATED IDENTITIES

We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with the q-group algebra. These apparently different results must agree, however, and their equivalence implies a q-identity. On letting q = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.