{
  "id": "math/0001161",
  "version": "v1",
  "published": "2000-01-28T10:55:38.000Z",
  "updated": "2000-01-28T10:55:38.000Z",
  "title": "The exterior algebra and `Spin' of an orthogonal g-module",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "LaTeX 2.09, 30 pages",
  "journal": "Transformation Groups, 6 (2001), 371-396",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "A well-known result of Kostant gives a description of the G-module structure for the exterior algebra of Lie algebra $\\frak g$. We give a generalization of this result for the isotropy representations of symmetric spaces. If $\\frak g={\\frak g}_0+{\\frak g_1}$ is a Z_2-grading of a simple Lie algebra, we explicitly describe a ${\\frak g}_0$-module $Spin_0({\\frak g}_1)$ such that the exterior algebra of ${\\frak g}_1$ is the tensor square of this module times some power of 2. Although $Spin_0({\\frak g}_1)$ is usually reducible, we show that a Casimir element for ${\\frak g}_0$ always acts scalarly on it. We also a give classification of all orthogonal representations of simple algebraic groups having an exterior algebra of skew-invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-28T10:55:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exterior algebra",
      "orthogonal g-module",
      "simple lie algebra",
      "simple algebraic groups",
      "isotropy representations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......1161P"
    }
  }
}