{
  "id": "2303.15897",
  "version": "v1",
  "published": "2023-03-28T11:22:41.000Z",
  "updated": "2023-03-28T11:22:41.000Z",
  "title": "${\\rm Spin}(7)$ is unacceptable",
  "authors": [
    "Gaëtan Chenevier",
    "Wee Teck Gan"
  ],
  "comment": "42 pages",
  "categories": [
    "math.NT",
    "math.GR",
    "math.RT"
  ],
  "abstract": "We classify the pairs of group morphisms $\\Gamma \\rightarrow {\\rm Spin}(7)$ which are element conjugate but not globally conjugate. As an application, we study the case where $\\Gamma$ is the Weil group of a $p$-adic local field, which is relevant to the recent approach to the local Langlands correspondence for ${\\rm G}_2$ and ${\\rm PGSp}_6$ by Gan and Savin. As a second application, we improve some result of Kret and Shin about ${\\rm GSpin}_7$-valued Galois representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T11:22:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22C05",
      "20G15",
      "20G41",
      "11F80",
      "11R39"
    ],
    "keywords": [
      "adic local field",
      "local langlands correspondence",
      "group morphisms",
      "element conjugate",
      "weil group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}