{
  "id": "0704.3494",
  "version": "v3",
  "published": "2007-04-26T08:10:04.000Z",
  "updated": "2008-04-16T16:48:05.000Z",
  "title": "Cherednik algebras for algebraic curves",
  "authors": [
    "Michael Finkelberg",
    "Victor Ginzburg"
  ],
  "comment": "final version",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "For any smooth algebraic curve C, Pavel Etingof introduced a `global' Cherednik algebra as a natural deformation of the cross product of the algebra of differential operators on C^n and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantumn Hamiltonian reduction. We study a category of character D-modules on a representation scheme associated to C and define a Hamiltonian reduction functor from that category to category O for the global Cherednik algebra. In the special case where the curve C is the multiplicative group, the global Cherednik algebra reduces to the trigonometric Cherednik algebra of type A, and our character D-modules become holonomic D-modules on GL_n \\times C^n. The corresponding perverse sheaves are reminiscent of (and include as special cases) Lusztig's character sheaves.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-16T16:48:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special case",
      "character d-modules",
      "global cherednik algebra reduces",
      "hamiltonian reduction functor",
      "trigonometric cherednik algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3494F"
    }
  }
}