Invariant Tensor Product

He H

Abstract

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1)×G(V2) be a pair of classical groups diagonally embedded in G(V1⊕V2). Suppose that dimV1<dimV2. Let π be a discrete series representation of G(V1⊕V2). We prove that the functor π ⊗G(V1) *maps unitary representations of G(V1) to unitary representations of G(V2). Here we enlarge the definition of unitary representations by including the zero dimensional representation.