{
  "id": "1812.00976",
  "version": "v1",
  "published": "2018-12-03T18:50:08.000Z",
  "updated": "2018-12-03T18:50:08.000Z",
  "title": "The Gelfand-Tsetlin Realisation of Simple Modules and Monomial Bases",
  "authors": [
    "Amadou Keita"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The most famous simple Lie algebra is $sl_n$ (the $n \\times n$ matrices with trace equals $0$). The representation theory for $sl_n$ has been one of the most important research areas for the past hundred years and within their the simple finite-dimensional modules have become very important. They are classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple module. We extend it by providing theorems and proofs, and construct monomial bases of the simple module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-03T18:50:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple module",
      "gelfand-tsetlin realisation",
      "construct monomial bases",
      "simple finite-dimensional modules",
      "famous simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}