{
  "id": "1403.7576",
  "version": "v1",
  "published": "2014-03-29T01:18:56.000Z",
  "updated": "2014-03-29T01:18:56.000Z",
  "title": "Conformal Oscillator Representations of Orthogonal Lie Algebras",
  "authors": [
    "Xiaoping Xu"
  ],
  "comment": "13pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o(n+2). Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a, we prove that the space forms an irreducible o(n+2)-module for any constant c if the vector a is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o(n+2) on the polynomial algebra C in n variables. Moreover, we prove that the algebra C forms an infinite-dimensional irreducible weight o(n+2)-module with finite-dimensional weight subspaces if the constant c is not a half integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-29T01:18:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "orthogonal lie algebra",
      "conformal oscillator representations",
      "general differential operator representations",
      "inhomogeneous first-order differential operator representations",
      "finite-dimensional weight subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7576X"
    }
  }
}