{
  "abstract": "We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter. By analyzing the spectra of the R-matrices, we conclude that the first and the third series are associated with the symmetric tensor representations of the quantum groups U_q(sl(2)) and U_q(sl(2|1)), respectively. The other two series appear to be related to representations of quantum groups in the case where q is a root of unity. The elements of the second series are associated with nilpotent representations of U_q(sl(2)). We also check the correspondence between these R-matrices and link invariants. Applying the Reshetikhin-Turaev procedure to the first, second, and fourth sequences yields, respectively, colored Jones polynomials, ADO invariants, and Alexander polynomials. To our surprise, a similar calculation for the third series yields a trivial result, identically equal to 1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06274",
  "author_total": 2,
  "authors": [
    {
      "name": "Petr Pivovarov"
    },
    {
      "name": "Pavel Pyatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y49cxdfmye3e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06274",
  "fulltext_url": null,
  "id": "1y49cxdfmye3e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06274",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212049487",
  "pdf_url": "https://arxiv.org/pdf/2609.06274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1y49cxdfmye3e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.06274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Iterative construction of the R-matrices in arbitrary dimensions",
  "title_text": "Iterative construction of the R-matrices in arbitrary dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1y49cxdfmye3e",
  "venue": "arXiv",
  "versions": []
}