{
  "abstract": "Let $v$ be an indeterminate. We give a presentation of the mirabolic quantum Schur algebra $\\mathcal{MS}_v(2,d)$ in terms of generators and defining relations. More precisely, we determine the kernel of the natural epimorphism from Rosso's mirabolic quantum $\\mathfrak{sl}_2$, $\\mathbf U^{\\mathrm{mir}}_v(2)=\\langle e,f,k^{\\pm 1},\\ell\\rangle$, onto $\\mathcal{MS}_v(2,d)$. Setting $P_d(k)=\\prod_{r=0}^{d}(k-v^{2r-d})$ and $Q_d(k)=\\prod_{r=1}^{d}(k-v^{2r-d})$, we prove $\\mathcal{MS}_v(2,d)\\cong \\mathbf U^{\\mathrm{mir}}_v(2)/ \\left\\langle P_d(k),(\\ell-1)Q_d(k)\\right\\rangle$. We further determine the split Wedderburn decomposition of this quotient and provide an equivalent presentation in terms of weight idempotents.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08353",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongjia Chen"
    },
    {
      "name": "Jian Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a443jr13vnh80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08353",
  "fulltext_url": null,
  "id": "a443jr13vnh80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08353",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212069735",
  "pdf_url": "https://arxiv.org/pdf/2609.08353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a443jr13vnh80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Presenting mirabolic quantum Schur algebras $\\mathcal{MS}_v(2,d)$",
  "title_text": "Presenting mirabolic quantum Schur algebras ℳ𝒮_v(2,d)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a443jr13vnh80",
  "venue": "arXiv",
  "versions": []
}