{
  "id": "2410.13606",
  "version": "v1",
  "published": "2024-10-17T14:43:05.000Z",
  "updated": "2024-10-17T14:43:05.000Z",
  "title": "Arthur packets for metaplectic groups",
  "authors": [
    "Wen-Wei Li"
  ],
  "comment": "90 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "For metaplectic groups over a local field of characteristic zero, we define the Arthur packet attached to any Arthur parameter $\\psi$ as a multi-set of unitary genuine irreducible representations, characterized by endoscopic character relations. Over number fields, we obtain a multiplicity formula for the genuine discrete $L^2$-automorphic spectrum in terms of global Arthur parameters and $\\epsilon$-factors, by leveraging the trace formula for metaplectic groups. This confirms a conjecture of Gan, and extends earlier results of Gan-Ichino on the Shimura-Waldspurger correspondences, whereas their works play a critical role in our proof. Furthermore, all these are shown to be compatible with existing results in rank one (Waldspurger) and two (Gan-Ichino).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-17T14:43:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70",
      "11F72"
    ],
    "keywords": [
      "metaplectic groups",
      "arthur packet",
      "extends earlier results",
      "unitary genuine irreducible representations",
      "global arthur parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 90,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}