{
  "id": "2304.03051",
  "version": "v1",
  "published": "2023-04-06T13:11:19.000Z",
  "updated": "2023-04-06T13:11:19.000Z",
  "title": "Matrix models for the nested hypergeometric tau-functions",
  "authors": [
    "Alexander Alexandrov"
  ],
  "comment": "26 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion formula. For arbitrary rational weight generating functions we construct the multi-matrix models. Two different types of cut-and-join descriptions are derived. Considered examples include generalized fully simple maps, which we identify with the recently introduced skew hypergeometric tau-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-06T13:11:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K10",
      "14N10",
      "81R10",
      "81T32",
      "05A15"
    ],
    "keywords": [
      "nested hypergeometric tau-functions",
      "matrix models",
      "skew schur function expansion formula",
      "arbitrary rational weight generating functions",
      "2d toda hierarchy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}