{
  "abstract": "We study determinantial modules associated with open Richardson varieties of symmetric Kac--Moody type. For the seed obtained by the Bao--Ye--Ménard mutation procedure, we give an explicit bijection between its vertices and the positions complementary to the leftmost subexpression. Each initial variable is a multiplicity-one convolution factor of the corresponding determinantial module, and these determinantial modules are cluster monomials in that seed. We deduce that the quantum cluster algebra with non-invertible frozen variables embeds in the Grothendieck ring of $\\mathscr C_{w,v}$, with cluster monomials represented by real simple modules up to normalization. In finite $ADE$ type, we identify the seed with Leclerc's seed and obtain a monoidal categorification after localization at the frozen variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.05184",
  "author_total": 1,
  "authors": [
    {
      "name": "Yingjin Bi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6sbjw2k44rfnv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05184",
  "fulltext_url": null,
  "id": "6sbjw2k44rfnv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05184",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7163657756",
  "pdf_url": "https://arxiv.org/pdf/2606.05184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6sbjw2k44rfnv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2606.05184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type",
  "title_text": "Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/6sbjw2k44rfnv",
  "venue": "arXiv",
  "versions": []
}