{
  "id": "math/0207024",
  "version": "v2",
  "published": "2002-07-02T17:50:39.000Z",
  "updated": "2002-09-10T00:53:15.000Z",
  "title": "Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)",
  "authors": [
    "Jonathan Brundan"
  ],
  "comment": "Version 2: some minor corrections and updated references",
  "journal": "Advances Math. 182 (2004), 28-77.",
  "categories": [
    "math.RT"
  ],
  "abstract": "The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\\mathfrak q(n)$ over $\\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach relating the character problem to canonical bases of the quantized enveloping algebra $U_q(\\mathfrak b_{\\infty})$. We also formulate for the first time a conjecture for the characters of the infinite dimensional irreducible representations in the analogue of category $\\mathcal O$ for the Lie superalgebra $\\mathfrak{q}(n)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-09-10T00:53:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "lie superalgebra",
      "character formulae",
      "kazhdan-lusztig polynomials",
      "infinite dimensional irreducible representations",
      "character problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......7024B"
    }
  }
}