{
  "id": "1707.08937",
  "version": "v1",
  "published": "2017-07-27T17:18:24.000Z",
  "updated": "2017-07-27T17:18:24.000Z",
  "title": "Fourier coefficients attached to small automorphic representations of ${\\mathrm{SL}}_n(\\mathbb{A})$",
  "authors": [
    "Olof Ahlén",
    "Henrik P. A. Gustafsson",
    "Axel Kleinschmidt",
    "Baiying Liu",
    "Daniel Persson"
  ],
  "comment": "55 pages",
  "categories": [
    "math.RT",
    "hep-th",
    "math.NT"
  ],
  "abstract": "We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\\mathrm{SL}}_n(\\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-27T17:18:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E55",
      "11F30"
    ],
    "keywords": [
      "small automorphic representations",
      "fourier coefficients",
      "highly degenerate whittaker coefficients",
      "next-to-minimal automorphic representations",
      "maximal parabolic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}