{
  "id": "math/0507521",
  "version": "v1",
  "published": "2005-07-26T01:01:17.000Z",
  "updated": "2005-07-26T01:01:17.000Z",
  "title": "The Global Dimension of Schur Algebras for GL_2 and GL_3",
  "authors": [
    "Alison E. Parker"
  ],
  "comment": "uses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pages",
  "journal": "J. Algebra, 241 (2001), 340-378",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL_2 and SL_3. We use these to show that the global dimension of a Schur algebra for GL_2 and GL_3 is twice the good filtration dimension. To do this for SL_3, we give an explicit filtration of the modules \\nabla(\\lambda) by modules of the form \\nabla(\\mu)^F \\otimes L(\\nu) where \\mu is a dominant weight and \\nu is p-restricted.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-26T01:01:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G99",
      "20G05",
      "20G10",
      "20G42"
    ],
    "keywords": [
      "schur algebra",
      "global dimension",
      "weyl filtration dimension",
      "quasi-hereditary algebra",
      "first define"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7521P"
    }
  }
}