{
  "id": "0801.4136",
  "version": "v1",
  "published": "2008-01-27T15:21:34.000Z",
  "updated": "2008-01-27T15:21:34.000Z",
  "title": "Characteristic cycles of standard modules for the rational Cherednik algebra of type Z/lZ",
  "authors": [
    "Toshiro Kuwabara"
  ],
  "comment": "40 pages, To appear in J. Math. Kyoto Univ",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We study the representation theory of the rational Cherednik algebra $H_\\kappa = H_\\kappa({\\mathbb Z}_l)$ for the cyclic group ${\\mathbb Z}_l = {\\mathbb Z} / l {\\mathbb Z}$ and its connection with the geometry of the quiver variety $M_\\theta(\\delta)$ of type $A_{l-1}^{(1)}$. We consider a functor between the categories of $H_\\kappa$-modules with different parameters, called the shift functor, and give the condition when it is an equivalence of categories. We also consider a functor from the category of $H_\\kappa$-modules with good filtration to the category of coherent sheaves on $M_\\theta(\\delta)$. We prove that the image of the regular representation of $H_\\kappa$ by this functor is the tautological bundle on $M_\\theta(\\delta)$. As a corollary, we determine the characteristic cycles of the standard modules. It gives an affirmative answer to a conjecture given in [Gordon, arXiv:math/0703150v1] in the case of ${\\mathbb Z}_l$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-27T15:21:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G99",
      "14J60"
    ],
    "keywords": [
      "rational cherednik algebra",
      "characteristic cycles",
      "standard modules",
      "type z/lz",
      "representation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}