Unitary representations of the universal cover of SU(1,1) and tensor products

Abstract

In this paper we study the discrete spectrum of tensor products of irreducible unitary representations of the universal covering group of $SU(1,1)$. As a consequence of these results, we show that the set of smooth vectors of the tensor product intersects trivially some of the representations in the discrete spectrum. These results illustrate aspects of the much larger program of branching laws for reductive groups.