{
  "id": "1002.3457",
  "version": "v6",
  "published": "2010-02-18T09:15:50.000Z",
  "updated": "2011-12-07T14:04:00.000Z",
  "title": "A non-recursive criterion for weights of a highest weight module for an affine Lie algebra",
  "authors": [
    "O. Barshevsky",
    "M. Fayers",
    "M. Schaps"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\Lambda$ be a dominant integral weight of level $k$ for the affine Lie algebra $\\mathfrak g$ and let $\\alpha$ be a non-negative integral combination of simple roots. We address the question of whether the weight $\\eta=\\Lambda-\\alpha$ lies in the set $P(\\Lambda)$ of weights in the irreducible highest-weight module with highest weight $\\Lambda$. We give a non-recursive criterion in terms of the coefficients of $\\alpha$ modulo an integral lattice $kM$, where $M$ is the lattice parameterizing the abelian normal subgroup $T$ of the Weyl group. The criterion requires the preliminary computation of a set no larger than the fundamental region for $kM$, and we show how this set can be efficiently calculated.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-12-07T14:04:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67"
    ],
    "keywords": [
      "affine lie algebra",
      "highest weight module",
      "non-recursive criterion",
      "dominant integral weight",
      "abelian normal subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3457B"
    }
  }
}