{
  "id": "1109.6669",
  "version": "v2",
  "published": "2011-09-29T20:42:50.000Z",
  "updated": "2012-03-29T21:09:40.000Z",
  "title": "A Giambelli formula for even orthogonal Grassmannians",
  "authors": [
    "Anders S. Buch",
    "Andrew Kresch",
    "Harry Tamvakis"
  ],
  "comment": "28 pages; added appendix gives geometric description of Schubert varieties, correcting errors in arXiv:0809.4966",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the singular and quantum cohomology ring of X as a polynomial in certain special Schubert classes. Our analysis reveals a surprising relation between the Schubert calculus on even and odd orthogonal Grassmannians. We also study eta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-29T21:09:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "05E15",
      "14M15"
    ],
    "keywords": [
      "giambelli formula",
      "orthogonal grassmannian parametrizing isotropic subspaces",
      "schubert calculus",
      "study eta polynomials",
      "odd orthogonal grassmannians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6669B"
    }
  }
}