{
  "id": "1304.2693",
  "version": "v2",
  "published": "2013-04-09T18:45:52.000Z",
  "updated": "2013-12-23T13:05:48.000Z",
  "title": "Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations",
  "authors": [
    "Andrey Minchenko",
    "Alexey Ovchinnikov",
    "Michael F. Singer"
  ],
  "comment": "61 pages",
  "doi": "10.1093/imrn/rnt344",
  "categories": [
    "math.RT",
    "math.AC",
    "math.CA"
  ],
  "abstract": "We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending existing results, which were obtained for SL(2) in the case of just one derivation. As an application of the above bound, we develop an algorithm that tests whether the parameterized differential Galois group of a system of linear differential equations is reductive and, if it is, calculates it.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-23T13:05:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12H05",
      "12H20",
      "13N10",
      "20G05",
      "20H20",
      "34M15"
    ],
    "keywords": [
      "reductive linear differential algebraic groups",
      "parameterized linear differential equations",
      "galois group",
      "explicit sharp upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2693M"
    }
  }
}