{
  "id": "2304.13993",
  "version": "v1",
  "published": "2023-04-27T07:29:54.000Z",
  "updated": "2023-04-27T07:29:54.000Z",
  "title": "Fourier transform on a cone and the minimal representation of even orthogonal group",
  "authors": [
    "Nadya Gurevich",
    "David Kazhdan"
  ],
  "comment": "25 pages. To appear in Israel Journal of Mathematics",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be an even orthogonal quasi-split group defined over a local non-archimedean field $F$. We describe the subspace of smooth vectors of the minimal representation of $G(F),$ realized on the space of square-integrable functions on a cone. Our main tool is the Fourier transform on the cone, for which we give an explicit formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-27T07:29:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "minimal representation",
      "fourier transform",
      "orthogonal group",
      "local non-archimedean field",
      "orthogonal quasi-split group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}