{
  "id": "1604.07380",
  "version": "v1",
  "published": "2016-04-25T19:43:01.000Z",
  "updated": "2016-04-25T19:43:01.000Z",
  "title": "The center of small quantum groups I: the principal block in type A",
  "authors": [
    "Anna Lachowska",
    "You Qi"
  ],
  "comment": "43 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.AG",
    "math.QA"
  ],
  "abstract": "We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case of $\\mathfrak{sl}_3$ is computed explicitly, and further evidence of $\\mathfrak{sl}_4$ is sketched. This allows us to formulate the conjecture that, as a bigraded vector space, the center of a regular block of the small quantum $\\mathfrak{sl}_m$ at a root of unity is isomorphic to Haiman's diagonal coinvariant algebra for the symmetric group $S_{m}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-25T19:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "14L99",
      "20G05"
    ],
    "keywords": [
      "small quantum group",
      "principal block",
      "haimans diagonal coinvariant algebra",
      "complex semisimple lie algebra",
      "elementary algebraic method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407380L"
    }
  }
}