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
toshi@ms.u-tokyo.ac.jp
[Abstract-pdf]
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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