{
  "abstract": "We propose a new formula relating the rationalized Drinfeld associators obtained from the Knizhnik--Zamolodchikov equation to the quantum $6j$-symbols of the algebra $\\mathcal{U}_q(\\mathfrak{g})$: $ U_{q} = U \\cdot Φ^{KZ}_{\\mathbb{Q}} $. We prove this relation in the case of the $\\mathfrak{sl}_N$ Lie algebra for the tensor cube of the fundamental and the first symmetric representation. We also check it perturbatively for the $\\mathfrak{sl}_N$ algebra for representations $[2]\\otimes [1] \\otimes [1]$, $[2]\\otimes [2] \\otimes [1]$, the non-trivial cases with multiplicities --- $[2,1]^{\\otimes 3}$, $[2,2]^{\\otimes 3}$, and in the case of the $\\mathfrak{so}_5$ Lie algebra for the tensor cube of the fundamental representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08044",
  "author_total": 4,
  "authors": [
    {
      "name": "Elena Lanina"
    },
    {
      "name": "Artem Novokhatnii"
    },
    {
      "name": "Alexey Sleptsov"
    },
    {
      "name": "Radomir Stepanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04fhgc4kdzccp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08044",
  "fulltext_url": null,
  "id": "04fhgc4kdzccp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08044",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221029800",
  "pdf_url": "https://arxiv.org/pdf/2610.08044",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04fhgc4kdzccp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.08044",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08044"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "On connection between associators and 6j-symbols",
  "title_text": "On connection between associators and 6j-symbols",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/04fhgc4kdzccp",
  "venue": "arXiv",
  "versions": []
}