{
  "id": "1101.5848",
  "version": "v2",
  "published": "2011-01-31T05:11:10.000Z",
  "updated": "2013-08-03T06:20:58.000Z",
  "title": "Differential operators on quantized flag manifolds at roots of unity II",
  "authors": [
    "Toshiyuki Tanisaki"
  ],
  "comment": "42 pages, final version to appear in Nagoya Mathematical Journal. arXiv admin note: text overlap with arXiv:1002.0113",
  "categories": [
    "math.RT"
  ],
  "abstract": "We formulate a Beilinson-Bernstein type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twisted $D$-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-03T06:20:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "17B37"
    ],
    "keywords": [
      "differential operators",
      "fixed regular harish-chandra central character",
      "quantized enveloping algebra",
      "beilinson-bernstein type derived equivalence",
      "corresponding quantized flag manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.5848T"
    }
  }
}