Branching laws for discrete Wallach points

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ 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 of the Plancherel measure involves quotients of Γ -functions and the c-function for a symmetric cone of smaller rank. © 2010 Elsevier Inc. All rights reserved.