{
  "id": "2408.04196",
  "version": "v1",
  "published": "2024-08-08T03:31:36.000Z",
  "updated": "2024-08-08T03:31:36.000Z",
  "title": "Growth Problems for Representations of Finite Groups",
  "authors": [
    "David He"
  ],
  "comment": "18 pages, many figures, comments welcome",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We compute (exact and asymptotic) formulas for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero, we obtain in addition a general exact formula for the growth rate and give a complete solution to the growth problems in terms of the character table. We also provide code used to compute our formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-08T03:31:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N45",
      "18M05",
      "20C15",
      "20C20"
    ],
    "keywords": [
      "finite groups",
      "growth problems",
      "representations",
      "growth rate",
      "general exact formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}