{
  "id": "2004.05012",
  "version": "v1",
  "published": "2020-04-10T12:43:49.000Z",
  "updated": "2020-04-10T12:43:49.000Z",
  "title": "Weight zero in tensor-decomposable irreducible representations of simple algebraic groups",
  "authors": [
    "Alexander Baranov",
    "Alexandre Zalesski"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a simple algebraic group in defining characteristic $p>0$, and let $V$ be an irreducible $G$-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for $V$ to have the zero weight. In addition, we provide a uniform criterion for an irreducible representation of a simple Lie algebra over the complex numbers to have a multiple of a prescribed fundamental weight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-10T12:43:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G40"
    ],
    "keywords": [
      "simple algebraic group",
      "tensor-decomposable irreducible representations",
      "weight zero",
      "simple lie algebra",
      "tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}