{
  "id": "1202.3347",
  "version": "v1",
  "published": "2012-02-15T15:55:17.000Z",
  "updated": "2012-02-15T15:55:17.000Z",
  "title": "Indecomposable representations and oscillator realizations of the exceptional Lie algebra G_2",
  "authors": [
    "Hua-Jun Huang",
    "You-Ning Li",
    "Dong Ruan"
  ],
  "comment": "29 pages, 4 figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In this paper various representations of the exceptional Lie algebra G_2 are investigated in a purely algebraic manner, and multi-boson/multi-fermion realizations are obtained. Matrix elements of the master representation, which is defined on the space of the universal enveloping algebra of G_2, are explicitly determined. From this master representation, different indecomposable representations defined on invariant subspaces or quotient spaces with respect to these invariant subspaces are discussed. Especially, the elementary representations of G_2 are investigated in detail, and the corresponding six-boson realization is given. After obtaining explicit forms of all twelve extremal vectors of the elementary representation with the highest weight {\\Lambda}, all representations with their respective highest weights related to {\\Lambda} are systematically discussed. For one of these representations the corresponding five-boson realization is constructed. Moreover, a new three-fermion realization from the fundamental representation (0,1) of G_2 is constructed also.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-15T15:55:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B25",
      "16S30",
      "20C35"
    ],
    "keywords": [
      "exceptional lie algebra",
      "indecomposable representations",
      "oscillator realizations",
      "highest weight",
      "master representation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1140/epjp/i2013-13066-4",
      "journal": "European Physical Journal Plus",
      "year": 2013,
      "month": "Jun",
      "volume": 128,
      "pages": 66
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1089172,
      "adsabs": "2013EPJP..128...66H"
    }
  }
}