{
  "id": "math/0609349",
  "version": "v2",
  "published": "2006-09-13T15:58:18.000Z",
  "updated": "2006-10-02T18:47:34.000Z",
  "title": "On the multiplicities of the irreducible highest weight modules over Kac-Moody algebras",
  "authors": [
    "Sergey Mozgovoy"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We prove that the weight multiplicities of the integrable irreducible highest weight module over the Kac-Moody algebra associated to a quiver are equal to the root multiplicities of the Kac-Moody algebra associated to some enlarged quiver. To do this, we use the Kac conjecture for indivisible roots and a relation between the Poincare polynomials of quiver varieties and the Kac polynomials, counting the number of absolutely irreducible representations of the quiver over finite fields. As a corollary of this relation, we get an explicit formula for the Poincare polynomials of quiver varieties, which is equivalent to the formula of Hausel.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-02T18:47:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B67"
    ],
    "keywords": [
      "kac-moody algebra",
      "poincare polynomials",
      "quiver varieties",
      "integrable irreducible highest weight module",
      "root multiplicities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9349M"
    }
  }
}