{
  "id": "1710.02183",
  "version": "v1",
  "published": "2017-10-05T19:17:48.000Z",
  "updated": "2017-10-05T19:17:48.000Z",
  "title": "Computing weight $q$-multiplicities for the representations of the simple Lie algebras",
  "authors": [
    "Pamela E. Harris",
    "Erik Insko",
    "Anthony Simpson"
  ],
  "comment": "9 pages, code for program, and 5 tables for computation using exceptional Lie algebras",
  "categories": [
    "math.RT"
  ],
  "abstract": "The multiplicity of a weight $\\mu$ in an irreducible representation of a simple Lie algebra $\\mathfrak{g}$ with highest weight $\\lambda$ can be computed via the use of Kostant's weight multiplicity formula. This formula is an alternating sum over the Weyl group and involves the computation of a partition function. In this paper we consider a $q$-analog of Kostant's weight multiplicity and present a SageMath program to compute $q$-multiplicities for the simple Lie algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-05T19:17:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17-08"
    ],
    "keywords": [
      "simple lie algebra",
      "computing weight",
      "representation",
      "kostants weight multiplicity formula",
      "sagemath program"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}