{
  "id": "math/0610376",
  "version": "v2",
  "published": "2006-10-11T17:16:17.000Z",
  "updated": "2006-10-11T21:46:10.000Z",
  "title": "Elementary divisors of the Shapovalov form on the basic representation of Kac-Moody algebras",
  "authors": [
    "David Hill"
  ],
  "journal": "J. Algebra 319 (2008), 5208-5246",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We provide an algorithm to calculate the invariant factors of the Shapovalov form on the standard $\\Z$-lattice inside the basic representation of a Kac-Moody algebra of $ADE$ type, and give explicit formulae in some cases. The techniques developed reduce the problem to finding the invariant factors of a family of bilinear forms on the ring of symmetric functions, having Jack's symmetric functions as an orthonormal basis. These results have applications to the representation theory of Iwahori-Hecke algebras at roots of unity and the modular representation theory of symmetric groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-11T21:46:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67",
      "20G05"
    ],
    "keywords": [
      "kac-moody algebra",
      "shapovalov form",
      "basic representation",
      "elementary divisors",
      "invariant factors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10376H"
    }
  }
}