{
  "id": "2505.06463",
  "version": "v1",
  "published": "2025-05-09T23:09:01.000Z",
  "updated": "2025-05-09T23:09:01.000Z",
  "title": "Representation Theory of the Twisted Yangians in Complex Rank",
  "authors": [
    "Arun S. Kannan",
    "Shihan Kanungo"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\\mathfrak{gl}_t)$ of the general linear Lie algebra $\\mathfrak{gl}_t$ in complex rank using the techniques of ultraproducts. In particular, Kalinov classified the simple finite-length modules over $Y(\\mathfrak{gl}_t)$. In this paper, we define the notion of a twisted Yangian in Deligne's categories, and we extend these techniques to classify finite-length simple modules over the twisted Yangians $Y(\\mathfrak{o}_t)$ and $Y(\\mathfrak{sp}_t)$ of the orthogonal and symplectic Lie algebras $\\mathfrak{o}_t,\\mathfrak{sp}_t$ in complex rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T23:09:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex rank",
      "twisted yangian",
      "representation theory",
      "general linear lie algebra",
      "simple finite-length modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}