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Journal of Lie Theory 26 (2016), No. 4, 927--990
Copyright Heldermann Verlag 2016

Norm Computation and Analytic Continuation of Vector Valued Holomorphic Discrete Series Representations

Ryosuke Nakahama
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan

We compute explicitly the norm of the vector-valued holomorphic discrete series representations, when its K-type is "almost multiplicity-free". As an application, we discuss the properties of highest weight modules, such as unitarizability, reducibility and composition series.

Keywords: Holomorphic discrete series representations, highest weight modules, Jordan triple systems, composition series.

MSC: 22E45, 43A85, 17C30

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