{
  "id": "math/0412199",
  "version": "v1",
  "published": "2004-12-09T20:57:39.000Z",
  "updated": "2004-12-09T20:57:39.000Z",
  "title": "Laguerre Functions on Symmetric Cones and recursion relations in the Real Case",
  "authors": [
    "Michael Aristidou",
    "Mark Davidson",
    "Gestur 'Olafsson"
  ],
  "categories": [
    "math.CA",
    "math.RT"
  ],
  "abstract": "In this article we derive differential recursion relations for the Laguerre functions on the cone C of positive definite real matrices. The highest weight representations of the group Sp(n,R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain C+ i Sym(n,R). We then use the Laplace transform to carry the Lie algebra action over to L^2(C ,dm_t). The differential recursion relations result by restricting to a distinguished three dimensional subalgebra, which is isomorphic to sl(2,R).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-09T20:57:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "43A85",
      "32M15",
      "44A10"
    ],
    "keywords": [
      "laguerre functions",
      "real case",
      "symmetric cones",
      "differential recursion relations result",
      "highest weight representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12199A"
    }
  }
}