{
  "id": "0904.0787",
  "version": "v1",
  "published": "2009-04-05T15:33:22.000Z",
  "updated": "2009-04-05T15:33:22.000Z",
  "title": "Weyl submodules in restrictions of simple modules",
  "authors": [
    "Vladimir Shchigolev"
  ],
  "journal": "Journal of Algebra 321 (2009), no. 5, 1453 -1462",
  "doi": "10.1016/j.jalgebra.2008.11.034",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be an algebraically closed field of characteristic p>0. Suppose that SL_{n-1}(F) is naturally embedded into SL_n(F) (either in the top left corner or in the bottom right corner). We prove that certain Weyl modules over SL_{n-1}(F) can be embedded into the restriction L(\\omega)\\downarrow_{SL_{n-1}(F)}, where L(\\omega) is a simple SL_n(F)-module. This allows us to construct new primitive vectors in L(\\omega)\\downarrow_{\\SL_{n-1}(F)} from any primitive vectors in the corresponding Weyl modules. Some examples are given to show that this result actually works.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-05T15:33:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05"
    ],
    "keywords": [
      "simple modules",
      "weyl submodules",
      "restriction",
      "primitive vectors",
      "corresponding weyl modules"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0787S"
    }
  }
}