Journal of Lie Theory

no. 1
Bounded Multiplicity Theorems for Induction and Restriction
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 197-238
We prove a geometric criterion for the bounded multiplicity property of ``small'' infinite-dimensional representations of real reductive Lie groups in both induction and restrictions. Applying the criterion to symmetric pairs, we give a full description of the triples $H \subset G \supset G'$ such that any irreducible admissible representations of $G$ with $H$-distinguished vectors have the bounded multiplicity property when restricted to the subgroup $G'$. This article also completes the proof of the general results announced in a previous paper of the author [Advances Math. 388 (2021), art.\,no.\,107862].
DOI: 10.5802/jolt.1227
Classification: 22E46, 22E45, 53D50, 58J42, 53C50
Keywords: Branching law, multiplicity, reductive group, symmetric pair, visible action, spherical variety 
@article{JOLT_2022_32_1_a10,
     author = {T. Kobayashi},
     title = {Bounded {Multiplicity} {Theorems} for {Induction} and {Restriction}},
     journal = {Journal of Lie Theory},
     pages = {197--238},
     year = {2022},
     volume = {32},
     number = {1},
     doi = {10.5802/jolt.1227},
     zbl = {1493.22014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1227/}
}
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T. Kobayashi. Bounded Multiplicity Theorems for Induction and Restriction. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 197-238. doi: 10.5802/jolt.1227

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