{
  "id": "1205.0119",
  "version": "v3",
  "published": "2012-05-01T09:02:55.000Z",
  "updated": "2013-10-28T13:53:27.000Z",
  "title": "On a class of tensor product representations for the orthosymplectic superalgebra",
  "authors": [
    "Kevin Coulembier"
  ],
  "journal": "J. Pure Appl. Algebra 217 (2013), no. 5, 819-837",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce the spinor representations for osp(m|2n). These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup pair (Spin(m) x Mp(2n),osp(m|2n)). We prove that these spinor spaces are uniquely characterized as the completely pointed osp(m|2n)-modules. Then the tensor product of this representation with irreducible finite dimensional osp(m|2n)-modules is studied. Therefore we derive a criterion for complete reducibility of tensor product representations. We calculate the decomposition into irreducible osp(m|2n)-representations of the tensor product of the super spinor space with an extensive class of such representations and also obtain cases where the tensor product is not completely reducible.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-28T13:53:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "tensor product representations",
      "orthosymplectic superalgebra",
      "super spinor space",
      "spinor representations",
      "symplectic spinors"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jpaa.2012.09.009"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1113220,
      "adsabs": "2012arXiv1205.0119C"
    }
  }
}