{
  "id": "1308.3030",
  "version": "v2",
  "published": "2013-08-14T04:44:38.000Z",
  "updated": "2014-07-28T04:29:10.000Z",
  "title": "Irreducible Characters of Kac-Moody Lie superalgebras",
  "authors": [
    "Shun-Jen Cheng",
    "Jae-Hoon Kwon",
    "Weiqiang Wang"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a large family of irreducible highest weight modules over a symmetrizable Kac-Moody Lie superalgebra are then given in terms of Kazhdan-Lusztig polynomials for the first time. We formulate a notion of integrable modules over a symmetrizable Kac-Moody Lie superalgebra via super duality, and show that these integrable modules form a semisimple tensor subcategory, whose Littlewood-Richardson tensor product multiplicities coincide with those in the Kac-Moody algebra setting.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-28T04:29:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "irreducible characters",
      "symmetrizable kac-moody lie superalgebra",
      "littlewood-richardson tensor product multiplicities coincide",
      "semisimple tensor subcategory",
      "integrable modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.3030C"
    }
  }
}