{
  "id": "2208.08018",
  "version": "v1",
  "published": "2022-08-17T01:57:23.000Z",
  "updated": "2022-08-17T01:57:23.000Z",
  "title": "On Wronskians and $qq$-systems",
  "authors": [
    "Anton M. Zeitlin"
  ],
  "comment": "13 pages. arXiv admin note: text overlap with arXiv:2112.02711, arXiv:2108.04184",
  "categories": [
    "math.AG",
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We discuss the $qq$-systems, the functional form of the Bethe ansatz equations for the twisted Gaudin model from a new geometric point of view. We use a concept of $G$-Wronskians, which are certain meromorphic sections of principal $G$-bundles on the projective line. In this context, the $qq$-system, similar to its difference analog, is realized as the relation between generalized minors of the $G$-Wronskian. We explain the link between $G$-Wronskians and twisted $G$-oper connections, which are the traditional source for the $qq$-systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-17T01:57:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bethe ansatz equations",
      "meromorphic sections",
      "twisted gaudin model",
      "geometric point",
      "functional form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}