{
  "id": "2302.02492",
  "version": "v1",
  "published": "2023-02-05T21:51:54.000Z",
  "updated": "2023-02-05T21:51:54.000Z",
  "title": "A family of Spin(8) dual pairs: the case of real groups",
  "authors": [
    "Wee Teck Gan",
    "Hung Yean Loke",
    "Annegret Paul",
    "Gordan Savin"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Exceptional groups of type $E_6$ contain dual pairs where one member is $\\mathrm{Spin}(8)$, and the other is $T\\rtimes \\mathbb Z/2\\mathbb Z$, where $T$ is a two-dimensional torus and the non-trivial element in $\\mathbb Z/2\\mathbb Z$ acts on $T$ by the inverse involution. We describe the correspondence of representations arising by restricting the minimal representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-05T21:51:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "real groups",
      "contain dual pairs",
      "exceptional groups",
      "inverse involution",
      "non-trivial element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}