Transfer of Unitary Representations

Abstract

This paper has as its primary purpose a clear exposition of the idea in [21] which we describe as transfer between real forms of a semi-simple Lie group over $\bb{C}$. The basic point is that there are representations of one real form that can be more easily understood in the context of another real from. An interesting example is a minimal representation (that is annihilated by the Joseph ideal) of a split group over $\bb{R}$. In the case when the complexi.cation admits a Hermitian symmetric real form, minimal representations of that real form are part of the "analytic continuation of the holomorphic discrete series"(cf.[5]) ...