{
  "id": "math/0603125",
  "version": "v2",
  "published": "2006-03-06T00:33:14.000Z",
  "updated": "2006-03-31T19:58:43.000Z",
  "title": "Schubert polynomials for the affine Grassmannian",
  "authors": [
    "Thomas Lam"
  ],
  "comment": "24 pages. Section 4 rewritten; examples and references added or updated",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant and Kumar's nilHecke ring, work of Peterson on the homology of based loops on a compact group, and earlier work of ours on non-commutative k-Schur functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-03-31T19:58:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "14N15"
    ],
    "keywords": [
      "affine grassmannian",
      "schubert polynomials",
      "affine schur functions",
      "kumars nilhecke",
      "identify polynomial representatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3125L"
    }
  }
}