{
  "id": "1610.06948",
  "version": "v1",
  "published": "2016-10-21T20:42:51.000Z",
  "updated": "2016-10-21T20:42:51.000Z",
  "title": "Bases for spaces of highest weight vectors in arbitrary characteristic",
  "authors": [
    "Adam Dent",
    "Rudolf Tange"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let k be an algebraically closed field of arbitrary characteristic. First we give explicit bases for the highest weight vectors for the action of GL_r x GL_s on the coordinate ring k[Mat_{rs}^m] of m-tuples of r x s-matrices. It turns out that this is done most conveniently by giving an explicit good GL_r x GL_s-filtration on k[Mat_{rs}^m]. Then we deduce from this result explicit spanning sets of the k[Mat_n]^{GL_n}-modules of highest weight vectors in the coordinate ring k[Mat_n] under the conjugation action of GL_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-21T20:42:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A50",
      "16W22",
      "20G05"
    ],
    "keywords": [
      "highest weight vectors",
      "arbitrary characteristic",
      "result explicit spanning sets",
      "coordinate ring",
      "conjugation action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}