Branching laws for discrete Wallach points

Details Branching laws for discrete Wallach points Branching laws for discrete Wallach points

2009-06-30

arxiv.org/abs/0906.5580v1

Journal of Functional Analysis 258 (2010), pp. 3241-3265

Mathematics

Representation Theory

22 pages

Scientific paper

10.1016/j.jfa.2010.01.025

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain $V\oplus i\Omega$ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of $GL(\Omega)$. Using Riesz distributions, an explicit intertwining operator is constructed as an analytic continuation of an integral operator. The density for the Plancherel measure involves quotients of $\Gamma$-functions and the $c$-function for a symmetric cone of smaller rank.

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