{
  "id": "1411.4725",
  "version": "v1",
  "published": "2014-11-18T03:29:35.000Z",
  "updated": "2014-11-18T03:29:35.000Z",
  "title": "Vertex operators arising from Jacobi-Trudi identities",
  "authors": [
    "Naihuan Jing",
    "Natasha Rozhkovskaya"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi-Trudi identity. This viewpoint enables us to formulate a unified theory of generalized Schur symmetric functions and obtain a generalized Giambelli identity. It also allows us to construct the action of the Clifford algebra (fermions) on the polynomial algebra from a generalized version of the Jacobi-Trudi identity. As applications, we obtain explicit vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-18T03:29:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "17B65",
      "17B69",
      "11C20"
    ],
    "keywords": [
      "jacobi-trudi identity",
      "vertex operators arising",
      "generalized schur symmetric functions",
      "linear recurrence relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.4725J",
      "inspire": 1422386
    }
  }
}