{
  "id": "math/0402089",
  "version": "v2",
  "published": "2004-02-05T22:58:17.000Z",
  "updated": "2004-12-23T20:54:16.000Z",
  "title": "Lie Superalgebras, Clifford Algebras, Induced Modules and Nilpotent Orbits",
  "authors": [
    "Ian M. Musson"
  ],
  "comment": "Accepted for publication in Advances in Mathematics. Some minor changes have been made to the original version, mostly in the last section",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\\cal O$ in $\\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\\cal O$. We find the rank, $k(\\cal O)$ of the bilinear form defining this Clifford algebra, and deduce a lower bound on the multiplicity of a $U(\\FRAK{g})$-module with $\\cal O$ or an orbital subvariety of $\\cal O$ as associated variety. In some cases we obtain modules where the lower bound on multiplicity is attained using parabolic induction. The invariant $k(\\cal O)$ is in many cases, equal to the odd dimension of the orbit $G\\cdot\\cal O$ where $G$ is a Lie supergroup with Lie superalgebra ${\\mathfrak g.}$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-12-23T20:54:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35"
    ],
    "keywords": [
      "clifford algebra",
      "nilpotent orbit",
      "induced modules",
      "lower bound",
      "classical simple lie superalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2089M"
    }
  }
}