{
  "id": "2408.16960",
  "version": "v1",
  "published": "2024-08-30T01:26:48.000Z",
  "updated": "2024-08-30T01:26:48.000Z",
  "title": "Generalized Green functions and unipotent classes for finite reductive groups, IV",
  "authors": [
    "Frank Lübeck",
    "Toshiaki Shoji"
  ],
  "comment": "71 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where $G$ is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for $G$ of type $E_7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-30T01:26:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G40"
    ],
    "keywords": [
      "generalized green functions",
      "unipotent class",
      "finite reductive groups",
      "split elements",
      "lusztigs algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}