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Journal of Lie Theory 33 (2023), No. 1, 305--328
Copyright Heldermann Verlag 2023

Bounded Multiplicity Branching for Symmetric Pairs

Toshiyuki Kobayashi
Graduate School of Mathematical Sciences, The University of Tokyo, Japan, Japan


We prove that any simply connected non-compact semisimple Lie group $G$ admits an infinite-dimensional irreducible representation $\Pi$ with bounded multiplicity property of the restriction $\Pi|_{G'}$ for {\it all} symmetric pairs $(G, G')$. We also discuss which irreducible representations $\Pi$ satisfy the bounded multiplicity property.

Keywords: Branching problem, symmetric pair, reductive group, visible action, spherical variety, multiplicity, minimal representation.

MSC: 22E46; 22E45, 53C35, 32M15, 53C15.

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