{
  "id": "1105.5500",
  "version": "v5",
  "published": "2011-05-27T08:58:09.000Z",
  "updated": "2014-01-20T18:44:01.000Z",
  "title": "Category O for quantum groups",
  "authors": [
    "Henning Haahr Andersen",
    "Volodymyr Mazorchuk"
  ],
  "comment": "To appear in JEMS. Some problems in formulation of Corollary 5.3 and formulation and proof of Theorem 6.2 fixed",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In this paper we study of the BGG-categories $\\mathcal O_q$ associated to quantum groups. We prove that many properties of the ordinary BGG-category $\\mathcal O$ for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when $q$ is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for $\\mathcal O$ and for finite dimensional $U_q$-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in $\\mathcal O_q$. As a consequence of our study of the root of unity case we deduce that the non-root of unity case (including the generic case) behaves like $\\mathcal O$.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-01-20T18:44:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum groups",
      "semisimple complex lie algebra carry",
      "indecomposable tilting modules",
      "unity case",
      "generic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5500H"
    }
  }
}