%0 Journal Article
%T Quantum Analogs of Tensor Product Representations of su(1,1)
%A Wolter Groenevelt
%J Mathematics
%D 2011
%I arXiv
%R 10.3842/SIGMA.2011.077
%X We study representations of $U_q(su(1,1))$ 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 $U_q(su(1,1))$ 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.
%U http://arxiv.org/abs/1104.5101v2