{
  "id": "1103.2105",
  "version": "v3",
  "published": "2011-03-10T19:03:10.000Z",
  "updated": "2011-12-18T18:59:31.000Z",
  "title": "Extensions of differential representations of SL(2) and tori",
  "authors": [
    "Andrey Minchenko",
    "Alexey Ovchinnikov"
  ],
  "comment": "21 pages; few misprints corrected; Lemma 4.6 added",
  "journal": "Journal of the Institute of Mathematics of Jussieu, Volume 12, Issue 1, 2013, pp 199-224",
  "doi": "10.1017/S1474748012000692",
  "categories": [
    "math.RT",
    "math.CT",
    "math.GR"
  ],
  "abstract": "Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. The differential representation theory is a key to developing algorithms computing these groups. In the rational representation theory of algebraic groups, one starts with SL(2) and tori to develop the rest of the theory. In this paper, we give an explicit description of differential representations of tori and differential extensions of irreducible representation of SL(2). In these extensions, the two irreducible representations can be non-isomorphic. This is in contrast to differential representations of tori, which turn out to be direct sums of isotypic representations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-18T18:59:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12H05",
      "13N10",
      "20G05"
    ],
    "keywords": [
      "extensions",
      "linear differential algebraic groups",
      "measure differential algebraic dependencies",
      "irreducible representation",
      "rational representation theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2105M"
    }
  }
}