{
  "id": "2403.02434",
  "version": "v2",
  "published": "2024-03-04T19:32:42.000Z",
  "updated": "2024-05-14T12:40:37.000Z",
  "title": "On the character tables of the finite reductive groups $E_6(q)_{\\text{ad}}$ and ${^2\\!E}_6(q)_{\\text{ad}}$",
  "authors": [
    "Meinolf Geck"
  ],
  "comment": "30 pages; added appendix by Jonas Hetz on groups of type D5",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show how the character tables of the groups $E_6(q)_{\\text{ad}}$ and ${^2\\!E}_6(q)_{\\text{ad}}$ can be constructed, where $q$ is a power of~$2$. (Partial results are also obtained for any $q$ not divisible by~$3$.) This is based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus computations using Michel's version of {\\sf CHEVIE}. We also need some general results that are specific to semisimple groups which are not of simply connected type. A further crucial ingredient is the determination of the values of the unipotent characters on unipotent elements for groups of type $D_4$ and $D_5$ (in characteristic~$2$).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-05-14T12:40:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20G40"
    ],
    "keywords": [
      "finite reductive groups",
      "character tables",
      "partial results",
      "unipotent elements",
      "michels version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}