{
  "id": "math/0411304",
  "version": "v1",
  "published": "2004-11-13T10:12:09.000Z",
  "updated": "2004-11-13T10:12:09.000Z",
  "title": "Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra",
  "authors": [
    "Toshiyuki Tanisaki",
    "Nanhua Xi"
  ],
  "comment": "22pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant $K$-group of Steinberg's triple variety. The $K$-group is equipped with a filtration indexed by closed $G$-stable subvarieties of the nilpotent variety, where $G$ is the corresponding reductive algebraic group over $\\mathbb{C}$. In this paper we will show in the case of type $A$ that the filtration is compatible with the Kazhdan-Lusztig basis of the Hecke algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-13T10:12:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05"
    ],
    "keywords": [
      "affine hecke algebra",
      "kazhdan-lusztig basis",
      "geometric filtration",
      "steinbergs triple variety",
      "affine weyl group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11304T"
    }
  }
}