{
  "id": "1910.07198",
  "version": "v1",
  "published": "2019-10-16T07:41:30.000Z",
  "updated": "2019-10-16T07:41:30.000Z",
  "title": "On formal degrees of unipotent representations",
  "authors": [
    "Yongqi Feng",
    "Eric Opdam",
    "Maarten Solleveld"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let G be a reductive p-adic group which splits over an unramified extension of the ground field. Hiraga, Ichino and Ikeda conjectured that the formal degree of a square-integrable G-representation $\\pi$ can be expressed in terms of the adjoint $\\gamma$-factor of the enhanced L-parameter of $\\pi$. A similar conjecture was posed for the Plancherel densities of tempered irreducible G-representations. We prove these conjectures for unipotent G-representations. We also derive explicit formulas for the involved adjoint $\\gamma$-factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-16T07:41:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11S37",
      "20G25"
    ],
    "keywords": [
      "formal degree",
      "unipotent representations",
      "similar conjecture",
      "ground field",
      "reductive p-adic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}