{
  "id": "2506.19619",
  "version": "v1",
  "published": "2025-06-24T13:38:31.000Z",
  "updated": "2025-06-24T13:38:31.000Z",
  "title": "The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups",
  "authors": [
    "Giulio Ricci"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Given a $p$-adic connected split reductive group $\\mathcal{G},$ we use the local Langlands correspondence as defined by Reeder and by Aubert, Baum, Plymen and Solleveld, to prove the HII conjecture for irreducible discrete series representations contained in a principal series of $\\mathcal{G}$. We verify the predicted formula relating the formal degree of such representations to the adjoint $\\gamma$-factor of their associated Langlands parameter. First, we prove it under the assumption that the center of $\\mathcal{G}$ is connected, and then we generalize the result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-24T13:38:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22E50"
    ],
    "keywords": [
      "split p-adic groups",
      "principal series",
      "hiraga-ichino-ikeda conjecture",
      "local langlands correspondence",
      "irreducible discrete series representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}