{
  "id": "math/0111306",
  "version": "v1",
  "published": "2001-11-29T17:28:36.000Z",
  "updated": "2001-11-29T17:28:36.000Z",
  "title": "Cartan Determinants and Shapovalov forms",
  "authors": [
    "Jonathan Brundan",
    "Alexander Kleshchev"
  ],
  "journal": "Math. Ann. 324 (2002), 431-449.",
  "categories": [
    "math.RT"
  ],
  "abstract": "We compute the determinant of the Gram matrix of the Shapovalov form on weight spaces of the basic representation of an affine Kac-Moody algebra of ADE type (possibly twisted). As a consequence, we obtain explicit formulae for the determinants of the Cartan matrices of $p$-blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-29T17:28:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67",
      "20G05"
    ],
    "keywords": [
      "shapovalov form",
      "cartan determinants",
      "affine kac-moody algebra",
      "ade type",
      "basic representation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11306B"
    }
  }
}