{
  "id": "2303.10713",
  "version": "v1",
  "published": "2023-03-19T16:48:05.000Z",
  "updated": "2023-03-19T16:48:05.000Z",
  "title": "Wavefront Sets of Unipotent Representations of Reductive $p$-adic Groups II",
  "authors": [
    "Dan Ciubotaru",
    "Lucas Mason-Brown",
    "Emile Okada"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The wavefront set is a fundamental invariant of an admissible representation arising from the Harish-Chandra-Howe local character expansion. In this paper, we give a precise formula for the wavefront set of an irreducible representation of real infinitesimal character in Lusztig's category of unipotent representations. Our formula generalizes the main result of arXiv:2112.14354, where this formula was obtained in the Iwahori-spherical case. We deduce that for any irreducible unipotent representation with real infinitesimal character, the algebraic wavefront set is a singleton, verifying a conjecture of M\\oeglin and Waldspurger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-19T16:48:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "unipotent representation",
      "adic groups",
      "real infinitesimal character",
      "harish-chandra-howe local character expansion",
      "algebraic wavefront set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}