{
  "id": "2303.15596",
  "version": "v1",
  "published": "2023-03-27T20:59:52.000Z",
  "updated": "2023-03-27T20:59:52.000Z",
  "title": "Symmetric Powers",
  "authors": [
    "János Kollár",
    "Pham Huu Tiep"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\\mathbb{F}$, we show that any irreducible ${\\mathbb{F}}G$-module $W$ appears, as a submodule or a quotient, in $\\mathrm{Sym}^m(V)$ for some integer $1 \\leq m \\leq |G|$ (that may depend on $W$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T20:59:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20"
    ],
    "keywords": [
      "symmetric powers",
      "faithful finite-dimensional representation",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}