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arXiv · 0906.5580

Branching laws for discrete Wallach points

Stéphane Merigon·Henrik Seppänen
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Abstract

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain $V\oplus iΩ$ 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 $GL(Ω)$. 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 $Γ$-functions and the $c$-function for a symmetric cone of smaller rank.

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BibTeXRIS

Stéphane Merigon, Henrik Seppänen. 2009-06-30. Branching laws for discrete Wallach points. https://doi.org/10.1016/j.jfa.2010.01.025

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