{
  "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 $\\mathfrak{h}$-admissibility when the compact factor of $\\mathfrak{h}$ is maximal in some sense.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06458",
  "author_total": 1,
  "authors": [
    {
      "name": "Masatoshi Kitagawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2kgdrabt6yg5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06458",
  "fulltext_url": null,
  "id": "b2kgdrabt6yg5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06458",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212075845",
  "pdf_url": "https://arxiv.org/pdf/2609.06458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2kgdrabt6yg5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Criteria for discrete decomposability and admissibility in the branching problem",
  "title_text": "Criteria for discrete decomposability and admissibility in the branching problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/b2kgdrabt6yg5",
  "venue": "arXiv",
  "versions": []
}