{
  "id": "math/9911068",
  "version": "v1",
  "published": "1999-11-10T18:39:10.000Z",
  "updated": "1999-11-10T18:39:10.000Z",
  "title": "On the equivariant K-theory of the nilpotent cone",
  "authors": [
    "Viktor Ostrik"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG",
    "math.QA"
  ],
  "abstract": "Let G be a simple algebraic group over the complex numbers. Let N be the cone of nilpotent elements in the Lie algebra of G. Let K_{G x C^*}(N) denote the Grothendieck group of the category of G x C^*-equivariant coherent sheaves on N. In this note we construct a Kazhdan-Lusztig type canonical basis of K_{G x C^*}(N) over representation ring of C^*. This basis is parametrized by the set of dominant weights for G. On the other hand we conjecture that this basis is close to the basis consisting of irreducible G-equivariant bundles on nilpotent orbits. This would give us a natural construction of Lusztig's bijection between two sets: \\{dominant weights for G\\} and \\{pairs consisting of a nilpotent orbit O and irreducible G-equivariant bundle on O.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-10T18:39:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivariant k-theory",
      "nilpotent cone",
      "irreducible g-equivariant bundle",
      "nilpotent orbit",
      "kazhdan-lusztig type canonical basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11068O"
    }
  }
}