Quantum Analogs of Tensor Product Representations of su(1,1)

[摘要] 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.

[关键词] tensor product representations;Clebsch–Gordan coef ficients;big q-Jacobi functions