{
  "id": "math/0507558",
  "version": "v2",
  "published": "2005-07-27T11:25:12.000Z",
  "updated": "2006-07-04T05:10:19.000Z",
  "title": "A variant of the induction theorem for Springer representations",
  "authors": [
    "Toshiaki Shoji"
  ],
  "comment": "18 pages. In this revised version, some errors are corrected. In particular some restrictions are added to the main results",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let G be a simple algebraic group over C with the Weyl group W. For a unipotent element u of G, let B_u be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup W_L. Assume that u is in L and let B_u^L be the corresponding variety for L. The induction theorem of Springer representations describes the W-module structure of H*(B_u) in terms of the W_L-module structure of H*(B_u^L). In this paper, we prove a certain refinement of the induction theorem by considering the action of a cyclic group of order e on H^*(B_u). As a corollary, we obtain a description of the values of Green functions at e-th root of unity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-04T05:10:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G10",
      "20G40"
    ],
    "keywords": [
      "induction theorem",
      "springer representations",
      "simple algebraic group",
      "weyl group",
      "e-th root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7558S"
    }
  }
}