Invariant Tensor Product

Abstract

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V 1 )×G(V 2 ) be a pair of classical groups diagonally embedded in G(V 1 ⊕V 2 ). Suppose that dimV 1 <dimV 2 . Let π be a discrete series representation of G(V 1 ⊕V 2 ). We prove that the functor