Highest-weight vectors in tensor products of Verma modules for U_q(sl_2)

Abstract

We obtain an explicit basis for the subspace spanned by highest-weight vectors in a tensor product of two highest-weight modules for the quantized universal enveloping algebra of sl_2. The structure constants provide a generalization of the Clebsh-Gordan coefficients. As a byproduct, we give an alternative proof for the decomposition of these tensor products as direct sums of indecomposable modules and supply generators for all highest weight summands.