{
  "id": "math/0703150",
  "version": "v1",
  "published": "2007-03-06T13:19:04.000Z",
  "updated": "2007-03-06T13:19:04.000Z",
  "title": "Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras",
  "authors": [
    "Iain Gordon"
  ],
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "We relate the representations of the rational Cherednik algebras associated with the complex reflection group G(m,1,n) to sheaves on Nakajima quiver varieties associated with extended Dynkin gaphs via a Z-algebra construction. As the parameters defining the Cherednik algebra vary, the stability conditions defining the quiver variety change. We interpret the ordering on category O geometrically using this relationship; we also relate the geometry to the a-function for Hecke algebras with unequal parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-06T13:19:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational cherednik algebras",
      "hecke algebras",
      "cherednik algebra vary",
      "complex reflection group",
      "quiver variety change"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3150G"
    }
  }
}