{
  "id": "1703.02457",
  "version": "v1",
  "published": "2017-03-07T16:33:32.000Z",
  "updated": "2017-03-07T16:33:32.000Z",
  "title": "On the center of the small quantum group II: singular blocks",
  "authors": [
    "Anna Lachowska",
    "You Qi"
  ],
  "comment": "35 pages, 3 figures, comments welcome",
  "categories": [
    "math.RT",
    "math.AG",
    "math.QA"
  ],
  "abstract": "We generalize to the case of singular blocks the result in \\cite{BeLa} that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in \\cite{LQ1}, we present a linear algebro-geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an $l$th root of unity is formulated in type A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T16:33:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "14L99",
      "20G05"
    ],
    "keywords": [
      "small quantum group",
      "singular blocks",
      "complex semisimple lie algebra",
      "linear algebro-geometric approach",
      "entire center"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}