{
  "id": "1006.4266",
  "version": "v1",
  "published": "2010-06-22T11:34:47.000Z",
  "updated": "2010-06-22T11:34:47.000Z",
  "title": "Plethysms, replicated Schur functions and series, with applications to vertex operators",
  "authors": [
    "Bertfried Fauser",
    "Peter D Jarvis",
    "Ronald C King"
  ],
  "comment": "36 pages, uses youngtab.tex",
  "journal": "J. Phys. A. Math and Theor. Vol 43, 2010, 405201",
  "doi": "10.1088/1751-8113/43/40/405202",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RA"
  ],
  "abstract": "Specializations of Schur functions are exploited to define and evaluate the Schur functions s_\\lambda[\\alpha X] and plethysms s_\\lambda[\\alpha s_\\nu(X))] for any \\alpha - integer, real or complex. Plethysms are then used to define pairs of mutually inverse infinite series of Schur functions, M_\\pi and L_\\pi, specified by arbitrary partitions \\pi. These are used in turn to define and provide generating functions for formal characters, s_\\lambda^{(\\pi)}, of certain groups H_\\pi, thereby extending known results for orthogonal and symplectic group characters. Each of these formal characters is then given a vertex operator realization, first in terms of the series M=M_{(0)} and various L_\\sigma^\\perp dual to L_\\sigma, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-22T11:34:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "17B69",
      "11E57",
      "16W30",
      "20E22",
      "33D52"
    ],
    "keywords": [
      "replicated schur functions",
      "formal characters",
      "applications",
      "vertex operator realization",
      "mutually inverse infinite series"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Oct",
      "volume": 43,
      "number": 40,
      "pages": 405202
    },
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43N5202F"
    }
  }
}