{
  "id": "1604.08911",
  "version": "v1",
  "published": "2016-04-29T17:00:21.000Z",
  "updated": "2016-04-29T17:00:21.000Z",
  "title": "Irreducibility of Weyl Modules over Fields of Arbitrary Characteristic",
  "authors": [
    "Skip Garibaldi",
    "Robert M. Guralnick",
    "Daniel K. Nakano"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In the representation theory of split reductive algebraic groups, it is well known that every Weyl module with minuscule highest weight is irreducible over every field. Also, the adjoint representation of $E_8$ is also irreducible over every field. In this paper, we prove a converse to these statements, as conjectured by Gross: if a Weyl module is irreducible over every field, it must be either one of these, or trivially constructed from one of these.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-29T17:00:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20C20"
    ],
    "keywords": [
      "weyl module",
      "arbitrary characteristic",
      "irreducibility",
      "minuscule highest weight",
      "split reductive algebraic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160408911G"
    }
  }
}