{
  "id": "math/0307383",
  "version": "v1",
  "published": "2003-07-30T05:13:28.000Z",
  "updated": "2003-07-30T05:13:28.000Z",
  "title": "Representations of wreath products on cohomology of De Concini-Procesi compactifications",
  "authors": [
    "Anthony Henderson"
  ],
  "comment": "38 pages",
  "journal": "Intern. Math. Res. Notices 2004:20 (2004), 983-1021",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "The wreath product W(r,n) of the cyclic group of order r and the symmetric group S_n acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula for the characters of the representations of W(r,n) on the cohomology groups of this compactification, extending the result of Ginzburg and Kapranov in the r=1 case. As a corollary, we get a formula for the Betti numbers which generalizes the result of Yuzvinsky in the r=2 case. Our method involves applying to the nested-set stratification a generalization of Joyal's theory of tensor species, which includes a link between polynomial functors and plethysm for general r. We also give a new proof of Lehrer's formula for the representations of W(r,n) on the cohomology groups of the hyperplane complement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-30T05:13:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "14D99",
      "05A15"
    ],
    "keywords": [
      "wreath product",
      "concini-procesi compactifications",
      "representations",
      "cohomology groups",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7383H"
    }
  }
}