{
  "id": "2301.13092",
  "version": "v1",
  "published": "2023-01-30T17:30:22.000Z",
  "updated": "2023-01-30T17:30:22.000Z",
  "title": "A Converse Theorem for Split $\\mathrm{SO}_{2l}$ over Finite Fields",
  "authors": [
    "Alexander Hazeltine",
    "Baiying Liu"
  ],
  "comment": "To appear in Acta Mathematica Sinica, English Series",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-30T17:30:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20G40"
    ],
    "keywords": [
      "converse theorem",
      "finite fields",
      "special orthogonal groups",
      "case left",
      "split classical groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}