We study representations of Uq(su(1,1)) that can be considered as quantum
analogs of tensor products of irreducible *-representations of the Lie algebra
su(1,1). We determine the decomposition of these representations into
irreducible *-representations of Uq(su(1,1)) by diagonalizing the action of
the Casimir operator on suitable subspaces of the representation spaces. This
leads to an interpretation of the big q-Jacobi polynomials and big q-Jacobi
functions as quantum analogs of Clebsch-Gordan coefficients