{
  "id": "1907.12198",
  "version": "v1",
  "published": "2019-07-29T03:30:11.000Z",
  "updated": "2019-07-29T03:30:11.000Z",
  "title": "Incarnations of XXX $\\widehat{\\frak{sl}_N}$ Bethe ansatz equations and integrable hierarchies",
  "authors": [
    "Igor Krichever",
    "Alexander Varchenko"
  ],
  "comment": "Latex, 57 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "nlin.SI"
  ],
  "abstract": "We consider the space of solutions of the Bethe ansatz equations of the $\\widehat{\\frak{sl}_N}$ XXX quantum integrable model, associated with the trivial representation of $\\widehat{\\frak{sl}_N}$. We construct a family of commuting flows on this space and identify the flows with the flows of coherent rational Ruijesenaars-Schneider systems. For that we develop in full generality the spectral transform for the rational Ruijesenaars-Schneider system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-29T03:30:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bethe ansatz equations",
      "integrable hierarchies",
      "incarnations",
      "coherent rational ruijesenaars-schneider systems",
      "xxx quantum integrable model"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}