Asian Journal of Mathematics

Volume 8 (2004)

Number 4

Transfer of Unitary Representations

Pages: 861 – 880

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n4.a28

Authors

Nolan R. Wallach

Chen-Bo Zhu

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]) ...

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