{
  "id": "2006.11491",
  "version": "v1",
  "published": "2020-06-20T04:21:21.000Z",
  "updated": "2020-06-20T04:21:21.000Z",
  "title": "Differential operators on quantized flag manifolds at roots of unity III",
  "authors": [
    "Toshiyuki Tanisaki"
  ],
  "comment": "39 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe the cohomology of the sheaf of twisted differential operators on the quantized flag manifold at a root of unity whose order is a prime power. It follows from this and our previous results that for the De Concini-Kac type quantized enveloping algebra, where the parameter $q$ is specialized to a root of unity whose order is a prime power, the number of irreducible modules with a certain specified central character coincides with the dimension of the total cohomology group of the corresponding Springer fiber. This gives a weak version of a conjecture of Lusztig concerning non-restricted representations of the quantized enveloping algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-20T04:21:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantized flag manifold",
      "differential operators",
      "prime power",
      "concini-kac type quantized enveloping algebra",
      "specified central character coincides"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}