{
  "id": "0710.1443",
  "version": "v2",
  "published": "2007-10-08T18:55:52.000Z",
  "updated": "2008-01-09T00:10:22.000Z",
  "title": "Variations on themes of Kostant",
  "authors": [
    "Victor Ginzburg"
  ],
  "comment": "Final version to appear in a special volume dedicated to Bertram Kostant. It supercedes arXiv:math.AG/9803141",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form Sym(g^e)/J. Here, J is an appropriate ideal in the symmetric algebra of g^e, the centralizer of a principal nilpotent in g. We also discuss a `topological' proof of Kostant's famous result on the structure of the polynomial algebra on g.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-09T00:10:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variations",
      "complex semisimple lie algebra",
      "langlands dual group",
      "arbitrary spherical schubert variety",
      "symmetric algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1443G"
    }
  }
}