{
  "id": "2101.04578",
  "version": "v1",
  "published": "2021-01-12T16:18:18.000Z",
  "updated": "2021-01-12T16:18:18.000Z",
  "title": "Toward the endoscopic classification of unipotent representations of $p$-adic $G_2$",
  "authors": [
    "Clifton Cunningham",
    "Andrew Fiori",
    "Qing Zhang"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "In this paper, we review the Langlands correspondence for unipotent representations of the exceptional group of type $G_2$ over a $p$-adic field $F$ and present it in an explicit form. Then we compute all ABV-packets, as introduced in [CFM+21] following ideas from Vogan's 1993 paper The Langlands Correspondence, for these representations and prove that these packets satisfy properties derived from the expectation that they are generalized A-packets. We attach distributions to ABV-packets for $G_2$ and its endoscopic groups and study a geometric endoscopic transfer of the distributions. This paper builds on earlier work by the same authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T16:18:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E50",
      "32S30",
      "32S60"
    ],
    "keywords": [
      "unipotent representations",
      "endoscopic classification",
      "langlands correspondence",
      "geometric endoscopic transfer",
      "packets satisfy properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}