{
  "abstract": "We prove a modified invertibility property for the parabolic defects introduced in arXiv:2102.12283, arXiv:2505.14836. Namely, we show that the Borel defect cancels its dual, up to insertion of an invertible Weyl defect and up to restriction to an open-subcategory. The main result holds for an arbitrary reductive group $G$ -- for illustration we give extended computations for $G=\\mathrm{SL}_3$. Along the way, we introduce a defect skein theory with defects in both codimension one and two, which is compatible with gluing of defect 3-manifolds and defect surfaces. Our results provide a potential defect skein theoretic construction of certain standard charts which appears frequently in quantum cluster varieties associated to surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09308",
  "author_total": 4,
  "authors": [
    {
      "name": "Jennifer Brown"
    },
    {
      "name": "Juan Ramón Gómez García"
    },
    {
      "name": "David Jordan"
    },
    {
      "name": "Matthias Vancraeynest"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44dma961ydevv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09308",
  "fulltext_url": null,
  "id": "44dma961ydevv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09308",
  "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": "W7212135802",
  "pdf_url": "https://arxiv.org/pdf/2609.09308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44dma961ydevv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weyl defects in skein theory and quantum cluster charts",
  "title_text": "Weyl defects in skein theory and quantum cluster charts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/44dma961ydevv",
  "venue": "arXiv",
  "versions": []
}