{
  "id": "1504.07859",
  "version": "v1",
  "published": "2015-04-29T13:52:31.000Z",
  "updated": "2015-04-29T13:52:31.000Z",
  "title": "Geometric approach to parabolic induction",
  "authors": [
    "David Kazhdan",
    "Yakov Varshavsky"
  ],
  "comment": "26 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "In this note we construct a \"restriction\" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to the parabolic induction and deduce that a parabolic induction preserves stability. We also give a new (purely geometric) proof that a character of the normalized parabolic induction does not depend on a parabolic subgroup. In the appendix, we use similar argument to extend a theorem of Lusztig-Spaltenstein on induced unipotent classes to all infinite fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-29T13:52:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric approach",
      "parabolic induction preserves stability",
      "dual map corresponds",
      "local non-archimedean field",
      "infinite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407859K"
    }
  }
}