{
  "abstract": "Let \\(G\\) be a simple and simply connected algebraic group of simply-laced type. For each positive braid word \\(β\\), and for the complete strong duality datum attached to a \\(Q\\)-datum, we construct an explicit based monoidal categorification of the quantum cluster algebra of the braid variety \\(X(β)\\). We identify this algebra with both a localized quantum Grothendieck ring and a localized level-\\(\\geq1\\) subalgebra of the bosonic extension algebra. Under these identifications, quantum cluster monomials correspond simultaneously to real simple modules and normalized global basis elements. We construct the specialization homomorphism at \\(q^{1/2}=1\\) and prove that it recovers \\(\\CC[X(β)]\\); in particular, the resulting integral form is a flat quantum deformation. We also give intrinsic Lusztig parameters for cluster variables attached to double strings, identify the corresponding quantum grid minors, and establish generalized quantum \\(T\\)-systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02962",
  "author_total": 1,
  "authors": [
    {
      "name": "Yingjin Bi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zzmrh06e6b7t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02962",
  "fulltext_url": null,
  "id": "4zzmrh06e6b7t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02962",
  "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": "W7208789813",
  "pdf_url": "https://arxiv.org/pdf/2609.02962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zzmrh06e6b7t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.02962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monoidal Categorification and Quantization of Braid Varieties",
  "title_text": "Monoidal Categorification and Quantization of Braid Varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4zzmrh06e6b7t",
  "venue": "arXiv",
  "versions": []
}