{
  "abstract": "We introduce the crystal groupoid of a compact semisimple Lie group $K$; it is the Deaconu-Renault groupoid of a higher-rank analogue of a subshift of finite type on an inverse limit of Kashiwara crystals. We show that its Steinberg algebra and its $C^*$-algebra realise the crystal limits of the polynomial function algebra of $K$ and its $C^*$-envelope, respectively, in the sense of Matassa and the second author. We show that the orbit space of the crystal groupoid is in bijection with the Weyl group of $K$, with topology determined by the Bruhat order on the Weyl group. We also define a crystal groupoid for flag manifolds and related Poisson homogeneous spaces, and prove the analogous structural results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01208",
  "author_total": 2,
  "authors": [
    {
      "name": "Aidan Sims"
    },
    {
      "name": "Robert Yuncken"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1kwd13sb6n76.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01208",
  "fulltext_url": null,
  "id": "a1kwd13sb6n76",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01208",
  "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"
    ],
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      "arxiv",
      "math.RT"
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    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
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  "openalex": "W7215799713",
  "pdf_url": "https://arxiv.org/pdf/2610.01208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1kwd13sb6n76.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01208"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The crystal groupoid of a compact semisimple Lie group and its flag varieties",
  "title_text": "The crystal groupoid of a compact semisimple Lie group and its flag varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/a1kwd13sb6n76",
  "venue": "arXiv",
  "versions": []
}