{
  "id": "2112.14354",
  "version": "v3",
  "published": "2021-12-29T01:26:45.000Z",
  "updated": "2022-03-14T09:51:45.000Z",
  "title": "Some Unipotent Arthur Packets for Reductive p-adic Groups I",
  "authors": [
    "Dan Ciubotaru",
    "Lucas Mason-Brown",
    "Emile Okada"
  ],
  "comment": "significantly revised exposition",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider Arthur's conjectures for split reductive $p$-adic groups from the point of view of the wavefront set, a fundamental invariant arising from the Harish-Chandra-Howe local character expansion of an admissible representation. We prove a precise formula for the wavefront set of an irreducible Iwahori-spherical representation with `real infinitesimal character' and determine a lower bound for this invariant in terms of the Kazhdan-Lusztig parameters. We define certain unipotent Arthur packets consisting of representations with minimal allowable wavefront sets, and we prove that their Iwahori-spherical constituents are the Aubert-Zelevinsky duals of tempered representations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-03-14T09:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "unipotent arthur packets",
      "reductive p-adic groups",
      "representation",
      "harish-chandra-howe local character expansion",
      "minimal allowable wavefront sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}