{
  "id": "1001.2490",
  "version": "v1",
  "published": "2010-01-14T15:46:18.000Z",
  "updated": "2010-01-14T15:46:18.000Z",
  "title": "Smooth Transfer (the Archimedean case)",
  "authors": [
    "Avraham Aizenbud",
    "Dmitry Gourevitch"
  ],
  "comment": "24 pages, no figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "We establish the existence of a transfer, which is compatible with Kloosterman integrals, between Schwartz functions on GL(n,R) and Schwartz functions on the variety of non-degenerate Hermitian forms. Namely, we consider an integral of a Schwartz function on GL(n,R) along the orbits of the two sided action of the groups of upper and lower unipotent matrices twisted by a non-degenerate character. This gives a smooth function on the torus. We prove that the space of all functions obtained in such a way coincides with the space that is constructed analogously when GL(n,R) is replaced with the variety of non-degenerate hermitian forms. We also obtain similar results for gl(n,R). The non-Archimedean case is done by Jacquet and our proof follows the same lines. However we have to face additional essential difficulties that appear only in the Archimedean case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-14T15:46:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G20",
      "22E30",
      "22E45"
    ],
    "keywords": [
      "archimedean case",
      "smooth transfer",
      "schwartz function",
      "non-degenerate hermitian forms",
      "face additional essential difficulties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.2490A"
    }
  }
}