Журнал обобщенной теории лжи и ее приложений

Invariant Tensor Product

Abstract

He H

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.