{
  "id": "1905.01414",
  "version": "v1",
  "published": "2019-05-04T02:30:04.000Z",
  "updated": "2019-05-04T02:30:04.000Z",
  "title": "Highest weight vectors in plethysms",
  "authors": [
    "Kazufumi Kimoto",
    "Soo Teck Lee"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We realize the $\\mathrm{GL}_n(\\mathbb{C})$-modules $S^k(S^m(\\mathbb{C}^n))$ and $\\Lambda^k(S^m(\\mathbb{C}^n))$ as spaces of polynomial functions on $n\\times k$ matrices. In the case $k=3$, we describe explicitly all the $\\mathrm{GL}_n(\\mathbb{C})$-highest weight vectors which occur in $S^3(S^m(\\mathbb{C}^n))$ and in $\\Lambda^3(S^m(\\mathbb{C}^n))$ respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-04T02:30:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20G05"
    ],
    "keywords": [
      "highest weight vectors",
      "polynomial functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}