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Criteria for discrete decomposability and admissibility in the branching problem

  • Masatoshi Kitagawa
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Abstract

In this paper, we study when the restriction of an irreducible representation of a reductive Lie group G to a reductive subgroup H is discretely decomposable. T.\ Kobayashi gave a necessary condition for discrete decomposability in terms of associated varieties. In a previous paper, we proved that the condition is also sufficient if $(G, H)$ is a symmetric pair. The purpose of this paper is to prove the sufficiency for any reductive subgroup H under some hypothesis on G (e.g., G is linear). As an application, we show that discrete decomposability is equivalent to h-admissibility when the compact factor of h is maximal in some sense.

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Cite

BibTeXRIS
BibTeX
@misc{kitagawa2026criteria,
  title = {{Criteria for discrete decomposability and admissibility in the branching problem}},
  author = {Masatoshi Kitagawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06458},
  eprint = {2609.06458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06458},
}
RIS
TY  - UNPB
TI  - Criteria for discrete decomposability and admissibility in the branching problem
AU  - Masatoshi Kitagawa
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06458
UR  - https://arxiv.org/abs/2609.06458
AB  - In this paper, we study when the restriction of an irreducible representation of a reductive Lie group G to a reductive subgroup H is discretely decomposable. T.\ Kobayashi gave a necessary condition for discrete decomposability in terms of associated varieties. In a previous paper, we proved that the condition is also sufficient if $(G, H)$ is a symmetric pair. The purpose of this paper is to prove the sufficiency for any reductive subgroup H under some hypothesis on G (e.g., G is linear). As an application, we show that discrete decomposability is equivalent to h-admissibility when the compact factor of h is maximal in some sense.
ER  -