{
  "abstract": "Given any tracial von Neumann algebra $\\mathcal{A}$, the first author has defined a unitary tensor functor $Φ:{\\rm Rep}(\\mathcal{Q}_{\\rm aut}(\\mathcal{A}))\\to {\\rm Bimod}(\\mathcal{A})$ in his paper [Gos24]. In this paper, we consider $\\mathcal{A}$ to be the underlying von Neumann algebra of $C^*(S_3)$ and show that given any DQG $\\mathcal{Q}$, which contains $C^*(S_3)$ as a quantum subgroup and has an outer action $\\tildeΦ$ (in the sense of Definition 3.4}) on ${\\rm Bimod}(\\mathcal{A})$, which agrees with $Φ$ when restricted on ${\\rm Rep}(C^*(S_3))$, is monoidally equivalent to the DQG $C^*(S_3)$. Furthermore, given any DQG $\\mathcal{Q}$ with an outer action $Γ:{\\rm Rep}(\\mathcal{Q})\\to {\\rm Bimod}(\\mathcal{A})$, such that $ {\\rm Out}(\\mathcal{A})\\subseteq {\\rm Im}(Γ)$, is either monoidally equivalent to Out$(\\mathcal{A})$ or monoidally equivalent to $C^*(S_3)$ itself.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39254",
  "author_total": 2,
  "authors": [
    {
      "name": "Debashish Goswami"
    },
    {
      "name": "Suchetana Samadder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4exaq1nb2m85w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39254",
  "fulltext_url": null,
  "id": "4exaq1nb2m85w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39254",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7215116347",
  "pdf_url": "https://arxiv.org/pdf/2609.39254",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4exaq1nb2m85w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39254",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39254"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Outer action of representation category of discrete quantum groups: a case study",
  "title_text": "Outer action of representation category of discrete quantum groups: a case study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/4exaq1nb2m85w",
  "venue": "arXiv",
  "versions": []
}