{
  "abstract": "We study twisted Yangians associated with the split symmetric pairs of types BI, CI and DI. We introduce a new presentation of these algebras, which we call the transposed presentation, governed by a twisted reflection equation that interacts naturally with the Gaussian decomposition of the generating matrix. Working entirely within the $R$-matrix presentation, we derive Drinfeld-type current presentations of the special twisted Yangian $SY^{\\mathrm{tw}}(\\mathfrak{g}_N)$ and of the extended twisted Yangian $X^{\\mathrm{tw}}(\\mathfrak{g}_N)$, in which the Serre relations are stated in a closed current form. Extracting coefficients recovers the Drinfeld presentation of Lu, Wang and Zhang, in the normalisation of Lu. As a consequence, we establish an explicit isomorphism between the $R$-matrix and Drinfeld presentations conjectured by Lu, Wang and Zhang. As a byproduct, we obtain a tensor product decomposition of $X^{\\mathrm{tw}}(\\mathfrak{g}_N)$ into the twisted Yangian in the Drinfeld presentation and a polynomial ring in countably many central variables. We also obtain Poincaré-Birkhoff-Witt bases in the Drinfeld generators and the coideal coproduct on the low Drinfeld modes at all but the last node.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.14692",
  "author_total": 1,
  "authors": [
    {
      "name": "Vidas Regelskis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7gr9qrh3cb5xm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.14692",
  "fulltext_url": null,
  "id": "7gr9qrh3cb5xm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.14692",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7169563942",
  "pdf_url": "https://arxiv.org/pdf/2607.14692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7gr9qrh3cb5xm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2607.14692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.14692"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations",
  "title_text": "Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7gr9qrh3cb5xm",
  "venue": "arXiv",
  "versions": []
}