{
  "id": "1207.2216",
  "version": "v2",
  "published": "2012-07-10T04:51:35.000Z",
  "updated": "2013-10-29T14:22:14.000Z",
  "title": "Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes",
  "authors": [
    "Hiraku Abe",
    "Tomoo Matsumura"
  ],
  "comment": "17 pages. Comments are welcome",
  "categories": [
    "math.AT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "In this paper, we study the T_w-equivariant cohomology of the weighted Grassmannians wGr(d,n) introduced by Corti-Reid where T_w is the n-dimensional torus that naturally acts on wGr(d,n). We introduce the equivariant weighted Schubert classes and, after we show that they form a basis of the equivariant cohomology, we give an explicit formula for the structure constants with respect to this Schubert basis. We also find a linearly independent subset {wu_1,...,wu_n} of Lie(T_w)^* such that those structure constants are polynomials in wu_i's with non-negative coefficients, up to a permutation on the weights.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-29T14:22:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "55N91",
      "57R18"
    ],
    "keywords": [
      "equivariant cohomology",
      "structure constants",
      "equivariant weighted schubert classes",
      "weighted grassmannians wgr",
      "schubert basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2216A"
    }
  }
}