{
  "id": "2301.05151",
  "version": "v1",
  "published": "2023-01-12T17:11:27.000Z",
  "updated": "2023-01-12T17:11:27.000Z",
  "title": "A local-global principle for unipotent characters",
  "authors": [
    "Damiano Rossi"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We obtain an adaptation of Dade's Conjecture and Sp\\\"ath's Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\\bf{A}$, $\\bf{B}$ and $\\bf{C}$. In particular, this gives a precise formula for counting the number of unipotent characters of each defect $d$ in any Brauer $\\ell$-block $B$ in terms of local invariants associated to $e$-local structures. This provides a geometric version of the local-global principle in representation theory of finite groups. A key ingredient in our proof is the construction of certain parametrisations of unipotent generalised Harish-Chandra series that are compatible with isomorphisms of character triples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-12T17:11:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "20C33"
    ],
    "keywords": [
      "unipotent characters",
      "local-global principle",
      "character triple conjecture",
      "unipotent generalised harish-chandra series",
      "simply connected finite reductive groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}