{
  "id": "2302.11842",
  "version": "v1",
  "published": "2023-02-23T08:13:00.000Z",
  "updated": "2023-02-23T08:13:00.000Z",
  "title": "Bethe vectors and recurrence relations for twisted Yangian based models",
  "authors": [
    "Vidas Regelskis"
  ],
  "comment": "25 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We study Olshanski twisted Yangian based models, known as one-dimensional \"soliton non-preserving\" open spin chains, by means of the algebraic Bethe ansatz. The even case, when the underlying bulk Lie algebra is $\\mathfrak{gl}_{2n}$, was studied in arXiv:1710.08409. In the present work, we focus on the odd case, when the underlying bulk Lie algebra is $\\mathfrak{gl}_{2n+1}$. We present a more symmetric form of the trace formula for Bethe vectors. We use the composite model approach and $Y(\\mathfrak{gl}_n)$-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-23T08:13:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B23",
      "17B37"
    ],
    "keywords": [
      "bethe vectors",
      "bulk lie algebra",
      "odd case",
      "study olshanski twisted yangian",
      "type recurrence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}