{
  "id": "math/0411127",
  "version": "v1",
  "published": "2004-11-06T05:07:10.000Z",
  "updated": "2004-11-06T05:07:10.000Z",
  "title": "On Ideal Generators for Affine Schubert Varieties",
  "authors": [
    "V. Kreiman",
    "V. Lakshmibai",
    "P. Magyar",
    "J. Weyman"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AG",
    "math.AC",
    "math.CO"
  ],
  "abstract": "We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by restricting certain Pl\\\"ucker co-ordinates. As a consequence, we write an explicit set of generators for the degree-one part of the ideal of the finite-dimensional embedding. This in turn gives a set of generators for the degree-one part of the ideal defining the affine Grassmannian inside the infinite Grassmannian which we conjecture to be a complete set of ideal generators. We apply our results to the orbit closures of nilpotent matrices. We describe (in a characteristic-free way) a filtration for the coordinate ring of a nilpotent orbit closure and state a conjecture on the SL(n)-module structures of the constituents of this filtration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-06T05:07:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15"
    ],
    "keywords": [
      "schubert variety",
      "affine schubert varieties",
      "ideal generators",
      "degree-one part",
      "affine grassmannian inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11127K"
    }
  }
}