{
  "abstract": "We study the twisted Yangian associated with the quasi-split symmetric pair $(\\mathfrak{o}_{2n}, \\mathfrak{o}_{n-1}\\oplus \\mathfrak{o}_{n+1})$ of type DI. Working in the transposed $R$-matrix presentation of arXiv:2607.14692, we show that the generating matrix $S(u)$ admits no Gaussian decomposition. We decompose instead the matrix $\\widehat{S}(u) = G\\,S(u)$, where $G$ is the constant term of $S(u)$. A chain of quasi-determinantal embeddings lowers the rank within this family of pairs and ends at $(\\mathfrak{o}_4,\\mathfrak{o}_3)$. Together with a direct study of a degenerate block of type AI, this gives a presentation of the special twisted Yangian $SY^{\\mathrm{tw}}(\\mathfrak{o}_{2n},\\mathfrak{o}_{n-1}\\oplus \\mathfrak{o}_{n+1})$ by Drinfeld type current relations. The two fork nodes of the Dynkin diagram carry Drinfeld's presentation of $Y(\\mathfrak{sl}_2)$. All other relations are those of split type DI, except that the Serre relation with a doubled fork node has zero right hand side. For $n\\ge3$ we obtain an explicit isomorphism between the $R$-matrix presentation of Guay and Regelskis and the Drinfeld presentation of Lu and Zhang. The Drinfeld generators are expressed through the Gaussian series of $\\widehat{S}(u)$. With quasi-split type AIII (Lu and Zhang), this completes the explicit comparison for the classical quasi-split types with a nontrivial diagram involution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08357",
  "author_total": 1,
  "authors": [
    {
      "name": "Vidas Regelskis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cynng95n174dx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08357",
  "fulltext_url": null,
  "id": "cynng95n174dx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08357",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08357",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cynng95n174dx.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08357",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08357"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Twisted Yangians of quasi-split type DI and Drinfeld type current relations",
  "title_text": "Twisted Yangians of quasi-split type DI and Drinfeld type current relations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/cynng95n174dx",
  "venue": "arXiv",
  "versions": []
}