{
  "id": "1310.7790",
  "version": "v4",
  "published": "2013-10-29T12:53:10.000Z",
  "updated": "2015-10-11T21:44:57.000Z",
  "title": "Spectral transfer morphisms for unipotent affine Hecke algebras",
  "authors": [
    "Eric Opdam"
  ],
  "comment": "61 pages; We explained the comparison with Lusztig's parameterization of unipotent representations in more detail",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we will give a complete classification of the spectral transfer morphisms between the unipotent affine Hecke algebras of the various inner forms of a given quasi-split absolutely simple algebraic group, defined over a non-archimidean local field $\\textbf{k}$ and split over an unramified extension of $\\textbf{k}$. As an application of these results, the results of [O4] on the spectral correspondences associated with such morphisms and some results of Ciubotaru, Kato and Kato [CKK] we prove a conjecture of Hiraga, Ichino and Ikeda [HII] on the formal degrees and adjoint gamma factors for all unipotent discrete series characters of unramified simple groups of adjoint type defined over $\\bf{k}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-22T10:30:19.000Z",
      "comment": "55 pages; We added more details to the computations of the rational factors of the formal degrees of discrete series",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-10-11T21:44:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22D25",
      "43A30"
    ],
    "keywords": [
      "unipotent affine hecke algebras",
      "spectral transfer morphisms",
      "quasi-split absolutely simple algebraic group",
      "unipotent discrete series characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7790O"
    }
  }
}