{
  "id": "1011.0509",
  "version": "v2",
  "published": "2010-11-02T04:36:10.000Z",
  "updated": "2011-05-25T03:25:49.000Z",
  "title": "Generic Representation Theory of the Additive and Heisenberg Groups",
  "authors": [
    "Michael Crumley"
  ],
  "comment": "This paper is being withdrawn because I recently discovered that almost half of the results contained therein are already known, and I do not wish to have them attributed to me. I plan on submitting an updated version of this paper, with proper citations",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we give an intimate connection between the characteristic zero representation theories of the Additive and Heisenberg groups, and their characteristic p >0 theories when p is much larger than the dimension a representation. In particular, if p >> dimension, then all characteristic p representations for these groups can be factored into commuting products of representations, with each factor arising from a representation of the Lie algebra of the group, one for each of the representation's Frobenius layers. In this sense, for a fixed dimension and large enough p, all representations for these groups look generically like representations for direct powers of themselves over a field of characteristic zero.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-25T03:25:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G15"
    ],
    "keywords": [
      "generic representation theory",
      "heisenberg groups",
      "characteristic zero representation theories",
      "representations frobenius layers",
      "lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0509C"
    }
  }
}