{
  "id": "1703.00046",
  "version": "v1",
  "published": "2017-02-25T10:30:05.000Z",
  "updated": "2017-02-25T10:30:05.000Z",
  "title": "The Malgrange form and Fredholm determinants",
  "authors": [
    "Marco Bertola"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We consider the factorization problem of matrix symbols depending analytically on parameters on a closed contour (i.e. a Riemann--Hilbert problem). We show how to define a function $\\tau$ which is locally analytic on the space of deformations and that is expressed as a Fredholm determinant of an operator of \"integrable\" type in the sense of Its-Izergin-Korepin-Slavnov. The construction is not unique and the non-uniqueness highlights the fact that the tau function is really the section of a line bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-25T10:30:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fredholm determinant",
      "malgrange form",
      "riemann-hilbert problem",
      "line bundle",
      "factorization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}