{
  "id": "1812.10226",
  "version": "v1",
  "published": "2018-12-26T05:01:24.000Z",
  "updated": "2018-12-26T05:01:24.000Z",
  "title": "Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences",
  "authors": [
    "Naoki Imai",
    "Takahiro Tsushima"
  ],
  "comment": "27 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We give a geometric construction of the Heisenberg-Weil representation of a finite unitary group by the middle \\'{e}tale cohomology of an algebraic variety over a finite field, whose rational points give a unitary Heisenberg group. Using also a Frobenius action, we give a geometric realization of the Howe correspondence for $(\\mathit{Sp}_{2n},O_2^-)$ over any finite field including characteristic two. As an application, we show that unipotency is preserved under the Howe correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-26T05:01:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "11F27"
    ],
    "keywords": [
      "finite unitary group",
      "howe correspondence",
      "heisenberg-weil representation",
      "geometric construction",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}