{
  "id": "1706.02243",
  "version": "v1",
  "published": "2017-06-07T16:27:10.000Z",
  "updated": "2017-06-07T16:27:10.000Z",
  "title": "Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra",
  "authors": [
    "Yusuke Ohkubo"
  ],
  "comment": "Based on Chapter 3 in arXiv:1703.10990. Theorem 4.4 is generalized. 24 pages, 3 figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA"
  ],
  "abstract": "In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level $N$ representation of the Ding-Iohara-Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-07T16:27:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kac determinant",
      "ding-iohara-miki algebra",
      "representation",
      "singular vectors correspond",
      "generalized macdonald functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}