{
  "id": "math/0203021",
  "version": "v1",
  "published": "2002-03-03T09:37:41.000Z",
  "updated": "2002-03-03T09:37:41.000Z",
  "title": "A Note on Principal Parts on Projective Space and Linear Representations",
  "authors": [
    "Helge Maakestad"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let H be a closed subgroup of a linear algebraic group G defined over a field F. There is an equivalence of categories between the category of linear finite-dimensional representations of H and the category of finite rank G-homogeneous vectorbundles on G/H. In this short note we study this correspondence for the sheaves of principal parts (=jetbundles) of homogeneous linebundles on projective space in characteristic zero. We describe the representation corresponding to the principal parts of a homogeneous linebundle and as a corollary we obtain known formulas on the splitting type of the principal parts on projective space in any dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-03T09:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "20G15"
    ],
    "keywords": [
      "principal parts",
      "projective space",
      "linear representations",
      "homogeneous linebundle",
      "linear algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3021M"
    }
  }
}