{
  "id": "0901.1506",
  "version": "v3",
  "published": "2009-01-12T05:30:56.000Z",
  "updated": "2009-08-31T23:52:35.000Z",
  "title": "K-theory Schubert calculus of the affine Grassmannian",
  "authors": [
    "Thomas Lam",
    "Anne Schilling",
    "Mark Shimozono"
  ],
  "comment": "38 pages",
  "journal": "Compositio Mathematica 146 Issue 4 (2010) 811-852",
  "doi": "10.1112/S0010437X09004539",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of Peterson in equivariant homology. For the case G = SL_n, the K-homology of the affine Grassmannian is identified with a sub-Hopf algebra of the ring of symmetric functions. The Schubert basis is represented by inhomogeneous symmetric functions, called K-k-Schur functions, whose highest degree term is a k-Schur function. The dual basis in K-cohomology is given by the affine stable Grothendieck polynomials, verifying a conjecture of Lam. In addition, we give a Pieri rule in K-homology. Many of our constructions have geometric interpretations using Kashiwara's thick affine flag manifold.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-31T23:52:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "14N15"
    ],
    "keywords": [
      "affine grassmannian",
      "k-theory schubert calculus",
      "kashiwaras thick affine flag manifold",
      "schubert basis",
      "symmetric functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.1506L"
    }
  }
}