{
  "id": "math/0604578",
  "version": "v2",
  "published": "2006-04-26T20:47:01.000Z",
  "updated": "2007-06-04T15:25:59.000Z",
  "title": "Permutation representations on Schubert varieties",
  "authors": [
    "Julianna S. Tymoczko"
  ],
  "comment": "20 pages, v2: minor revisions",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t_1, t_2,...,t_n]. We show these group actions are the same as an action of simple transpositions studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and others. We analyze these representations using the combinatorial approach to equivariant cohomology introduced by Goresky-Kottwitz-MacPherson. We find that each permutation representation on equivariant cohomology produces a representation on ordinary cohomology that is trivial, though the equivariant representation is not.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-04T15:25:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "05E10",
      "14M15",
      "55N91",
      "20F55"
    ],
    "keywords": [
      "schubert varieties",
      "studies permutation representations",
      "equivariant cohomology produces",
      "equivariant representation",
      "group actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4578T"
    }
  }
}