{
  "id": "2305.09076",
  "version": "v1",
  "published": "2023-05-16T00:11:48.000Z",
  "updated": "2023-05-16T00:11:48.000Z",
  "title": "Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields",
  "authors": [
    "Moshe Adrian",
    "Guy Henniart",
    "Eyal Kaplan",
    "Masao Oi"
  ],
  "comment": "52 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We consider the split special orthogonal group $\\mathrm{SO}_{N}$ defined over a $p$-adic field. We determine the structure of any $L$-packet of $\\mathrm{SO}_{N}$ containing a simple supercuspidal representation (in the sense of Gross--Reeder). We also determine its endoscopic lift to a general linear group. Combined with the explicit local Langlands correspondence for simple supercuspidal representations of general linear groups, this leads us to get an explicit description of the $L$-parameter as a representation of the Weil group of $F$. Our result is new when $p=2$ and our method provides a new proof even when $p\\neq2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-16T00:11:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70",
      "11L05"
    ],
    "keywords": [
      "split special orthogonal group",
      "simple supercuspidal l-packets",
      "dyadic fields",
      "simple supercuspidal representation",
      "general linear group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}