{
  "id": "1106.2586",
  "version": "v3",
  "published": "2011-06-14T00:45:06.000Z",
  "updated": "2015-02-07T01:05:23.000Z",
  "title": "Projected Richardson varieties and affine Schubert varieties",
  "authors": [
    "Xuhua He",
    "Thomas Lam"
  ],
  "comment": "20 pages. To appear in Annales de l'institut fourier",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "Let $G$ be a complex quasi-simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of $G$. Furthermore, we compare the torus-equivariant cohomology and $K$-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type $A$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-09T01:24:19.000Z",
      "abstract": "Let $G$ be a complex simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of $G$. Furthermore, we compare the torus-equivariant cohomology and $K$-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type $A$.",
      "comment": "20 pages. A new section on K-theory comparison is added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-07T01:05:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "05E10"
    ],
    "keywords": [
      "affine schubert varieties",
      "full flag variety form",
      "complex simple algebraic group",
      "projected richardson varieties agrees",
      "closure partial order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.2586H"
    }
  }
}