{
  "abstract": "We establish that the skew-symmetric bicharacter on the group of $\\ell$-weights of a quantum affine algebra is invariant under Chari's braid group action. Furthermore, we define an extension of this bicharacter to the group generated by prefundamental $\\ell$-weights and show that this invariance continues to hold under the extended braid group action of Frenkel-Hernandez. As immediate applications, we obtain braid group actions by automorphisms on the quantum tori associated respectively with the category of finite-dimensional representations of the quantum affine algebra and with the category $\\mathcal{O}^{\\mathfrak{b}}$ of its Borel subalgebra. In addition, we derive explicit formulas for quantum $QQ$-systems in all simply-laced types. Finally, we show that our extended bicharacter yields a quantization matrix compatible with the Hernandez-Leclerc cluster algebra categorified by $\\mathcal{O}^{\\mathfrak{b}}$ for all finite Dynkin types, extending Bittmann's construction in the simply-laced setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06384",
  "author_total": 1,
  "authors": [
    {
      "name": "Francesca Paganelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fyw5x7w1cfg8f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06384",
  "fulltext_url": null,
  "id": "fyw5x7w1cfg8f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06384",
  "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": "W7220715672",
  "pdf_url": "https://arxiv.org/pdf/2610.06384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fyw5x7w1cfg8f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Braid group invariance of quantum tori and applications",
  "title_text": "Braid group invariance of quantum tori and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/fyw5x7w1cfg8f",
  "venue": "arXiv",
  "versions": []
}