{
  "id": "math/0405444",
  "version": "v1",
  "published": "2004-05-23T23:39:11.000Z",
  "updated": "2004-05-23T23:39:11.000Z",
  "title": "Tensor product stabilization in Kac-Moody algebras",
  "authors": [
    "Michael Kleber",
    "Sankaran Viswanath"
  ],
  "comment": "33 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We consider a large class of series of symmetrizable Kac-Moody algebras (generically denoted X_n). This includes the classical series A_n as well as others like E_n whose members are of Indefinite type. The focus is to analyze the behavior of representations in the large n limit. Motivated by the classical theory of A_n, we consider tensor product decompositions of irreducible highest weight representations of X_n and study how these vary with n. The notion of ``double headed'' dominant weights is introduced. For such weights, we show that tensor product decompositions in X_n do stabilize, generalizing the classical results for A_n. The main tool used is Littelmann's celebrated path model. One can also use the stable multiplicities as structure constants to define a multiplication operation on a suitable space. We define this so called \"stable representation ring'' and show that the multiplication operation is associative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-23T23:39:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67"
    ],
    "keywords": [
      "tensor product stabilization",
      "tensor product decompositions",
      "multiplication operation",
      "irreducible highest weight representations",
      "littelmanns celebrated path model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5444K"
    }
  }
}