Branching laws for discrete Wallach points

Abstract

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.

22 pages

References in corpus (1)

• Branching of some holomorphic representations of SO(2,N)

Cited by in corpus (4)

• Discrete branching laws for minimal holomorphic representations
• Minimal representations of conformal groups and generalized Laguerre functions
• Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups
• Branching laws for small unitary representations of GL(n,C)