{
  "abstract": "We prove that the mirabolic Hecke algebra $\\mathscr{H}_{n,R}(q)$ over a commutative ring $R$ is cellular by constructing explicit cellular bases. When $R=\\mathbb{K}$ is a field, we also establish a Morita equivalence between $\\mathscr{H}_{n,\\mathbb{K}}(q)$ and a direct sum of Hecke algebras associated with symmetric groups. As applications, we classify the irreducible $\\mathscr{H}_{n,\\mathbb{K}}(q)$-modules and obtain a semisimplicity criterion. Finally, when $\\mathbb{K}=\\mathbb{C}(q)$, we show that the cell modules arising from one of our cellular bases coincide with Siegel's irreducible $\\mathscr{H}_{n,\\mathbb{K}}(q)$-modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25268",
  "author_total": 4,
  "authors": [
    {
      "name": "Jian Chen"
    },
    {
      "name": "Yan Liu"
    },
    {
      "name": "Jinkui Wan"
    },
    {
      "name": "Xirui Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frgbqr2k9829x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25268",
  "fulltext_url": null,
  "id": "frgbqr2k9829x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25268",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223003559",
  "pdf_url": "https://arxiv.org/pdf/2610.25268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frgbqr2k9829x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.25268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cellular bases of mirabolic Hecke algebras",
  "title_text": "Cellular bases of mirabolic Hecke algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/frgbqr2k9829x",
  "venue": "arXiv",
  "versions": []
}