{
  "id": "1804.04782",
  "version": "v1",
  "published": "2018-04-13T04:11:35.000Z",
  "updated": "2018-04-13T04:11:35.000Z",
  "title": "Remarks on irregular conformal blocks and Painlevé III and II tau functions",
  "authors": [
    "Hajime Nagoya"
  ],
  "comment": "11 pages, submitted to a proceeding of the workshop \"Meeting for Study of Number theory, Hopf algebras and related topics\", Toyama, 12-15 February 2017",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove a conjecture on uniqueness and existence of the irregular vertex operators of rank $r$ introduced in our previous paper. We also introduce ramified irregular vertex operators of the Virasoro algebra. As applications, we give conjectural formulas for series expansions of Painlev\\'e III and II tau functions in terms of our ramified irregular conformal blocks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T04:11:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tau functions",
      "ramified irregular vertex operators",
      "ramified irregular conformal blocks",
      "virasoro algebra",
      "conjectural formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}