{
  "abstract": "Given a morphism of Abe-Bott-Samelson bimodules, we construct an algorithm for computing its double-leaves coefficients. The key ingredient is a modification of Bruhat upper-triangularity which allows us to use forward substitution to solve for the double-leaf coefficients. We provide a complete implementation of the algorithm in the Sage computer algebra system. We use this to compute the Zamolodchikov 3-color relation in type $H_3$ for balanced realizations. We further simplify the 3-color relation using thick Soergel calculus and express it as a difference of two thick Elias--Williamson diagrams.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05299",
  "author_total": 1,
  "authors": [
    {
      "name": "Colton Sandvik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd9bzt6dbewwc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05299",
  "fulltext_url": null,
  "id": "fd9bzt6dbewwc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05299",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220654338",
  "pdf_url": "https://arxiv.org/pdf/2610.05299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd9bzt6dbewwc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Calculating double-leaf coefficients in the Hecke category",
  "title_text": "Calculating double-leaf coefficients in the Hecke category",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/fd9bzt6dbewwc",
  "venue": "arXiv",
  "versions": []
}