{
  "id": "math/0411424",
  "version": "v1",
  "published": "2004-11-19T02:11:45.000Z",
  "updated": "2004-11-19T02:11:45.000Z",
  "title": "The Chow ring of the classifying space $BSO(2n,{\\mathbb C})$",
  "authors": [
    "Rebecca E. Field"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We compute the Chow ring of the classifying space $BSO(2n,\\C)$ in the sense of Totaro using the fibration $Gl(2n)/SO(2n) \\to BSO(2n) \\to BGl(2n)$ and a computation of the Chow ring of $Gl(2n)/SO(2n)$ in a previous paper. We find this Chow ring is generated by Chern classes and a characteristic class defined by Edidin and Graham which maps to $2^{n-1}$ times the Euler class under the usual class map from the Chow ring to ordinary cohomology. Moreover, we show this class represents $1/2^{n-1}(n-1)!$ times the $n^{th}$ Chern class of the representation of SO(2n) whose highest weight vector is twice that of the half-spin representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-19T02:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14C15"
    ],
    "keywords": [
      "chow ring",
      "classifying space",
      "highest weight vector",
      "usual class map",
      "class represents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11424F"
    }
  }
}