{
  "id": "1208.3827",
  "version": "v1",
  "published": "2012-08-19T12:39:58.000Z",
  "updated": "2012-08-19T12:39:58.000Z",
  "title": "The orthosymplectic superalgebra in harmonic analysis",
  "authors": [
    "Kevin Coulembier"
  ],
  "comment": "partial overlap with arXiv:1202.0668",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce the orthosymplectic superalgebra osp(m|2n) as the algebra of Killing vector fields on Riemannian superspace R^{m|2n} which stabilize the origin. The Laplace operator and norm squared on R^{m|2n}, which generate sl(2), are orthosymplectically invariant, therefore we obtain the Howe dual pair (osp(m|2n),sl(2)). We study the osp(m|2n)-representation structure of the kernel of the Laplace operator. This also yields the decomposition of the supersymmetric tensor powers of the fundamental osp(m|2n)-representation under the action of sl(2) x osp(m|2n). As a side result we obtain information about the irreducible osp(m|2n)-representations L_(k,0,...,0). In particular we find branching rules with respect to osp(m-1|2n) and an interesting formula for the Cartan product inside the tensor powers of the natural representation of osp(m|2n). We also prove that integration over the supersphere is uniquely defined by its orthosymplectic invariance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-19T12:39:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "58C50"
    ],
    "keywords": [
      "orthosymplectic superalgebra",
      "harmonic analysis",
      "laplace operator",
      "cartan product inside",
      "howe dual pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3827C"
    }
  }
}