{
  "id": "1406.7502",
  "version": "v2",
  "published": "2014-06-29T13:11:49.000Z",
  "updated": "2014-08-22T05:43:29.000Z",
  "title": "Derived equivalences for Rational Cherednik algebras",
  "authors": [
    "Ivan Losev"
  ],
  "comment": "32 pages, preliminary version; v2 33 pages some proofs rewritten",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let W be a complex reflection group and H_c(W) the Rational Cherednik algebra for $W$ depending on a parameter c. One can consider the category O for H_c(W). We prove a conjecture of Rouquier that the categories O for H_c(W) and H_{c'}(W) are derived equivalent provided the parameters c,c' have integral difference. Two main ingredients of the proof are a connection between the Ringel duality and Harish-Chandra bimodules and an analog of a deformation technique developed by the author and Bezrukavnikov. We also show that some of the derived equivalences we construct are perverse.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-29T13:11:49.000Z",
      "comment": "32 pages, preliminary version",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-22T05:43:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E99",
      "16G99"
    ],
    "keywords": [
      "rational cherednik algebra",
      "derived equivalences",
      "complex reflection group",
      "ringel duality",
      "deformation technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7502L"
    }
  }
}