{
  "id": "1506.01992",
  "version": "v1",
  "published": "2015-06-05T17:42:18.000Z",
  "updated": "2015-06-05T17:42:18.000Z",
  "title": "Equivariant K-theory of Grassmannians",
  "authors": [
    "Oliver Pechenik",
    "Alexander Yong"
  ],
  "comment": "93 pages",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We address a unification of the Schubert calculus problems solved by [A. Buch '02] and [A. Knutson-T. Tao '03]. That is, we prove a combinatorial rule for the structure coefficients in the torus-equivariant K-theory of Grassmannians with respect to the basis of Schubert structure sheaves. We thereby deduce the conjectural rule of [H. Thomas-A. Yong '13] for the same coefficients. Both rules are positive in the sense of [D. Anderson-S. Griffeth-E. Miller '11] (and moreover in a stronger form). Our work is based on the combinatorics of genomic tableaux and a generalization of [M.-P. Schutzenberger '77]'s jeu de taquin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-05T17:42:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grassmannians",
      "schubert calculus problems",
      "schubert structure sheaves",
      "conjectural rule",
      "genomic tableaux"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 93,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150601992P"
    }
  }
}