Branching laws for discrete Wallach points |
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Authors: | Sté phane Merigon,Henrik Seppä nen |
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Affiliation: | a Fachbereich Mathematik, AG AGF, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany b Universität Paderborn, Fakultät für Elektrotechnik, Informatik und Mathematik, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany |
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Abstract: | 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. |
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Keywords: | Lie group Holomorphic discrete series Branching law Symmetric tube domains Jordan algebras Spherical functions Plancherel theorem |
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