{
  "id": "2309.14804",
  "version": "v1",
  "published": "2023-09-26T10:00:15.000Z",
  "updated": "2023-09-26T10:00:15.000Z",
  "title": "Generic direct summands of tensor productsfor simple algebraic groups and quantum groups",
  "authors": [
    "Jonathan Gruber"
  ],
  "comment": "24 pages, 1 figure, comments welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $\\mathbf{G}$ be either a simple linear algebraic group over an algebraically closed field of positive characteristic or a quantum group at a root of unity. We define new classes of indecomposable $\\mathbf{G}$-modules, which we call generic direct summands of tensor products because they appear generically in Krull-Schmidt decompositions of tensor products of simple $\\mathbf{G}$-modules and of Weyl modules. We establish a Steinberg-Lusztig tensor product theorem for generic direct summands of tensor products of simple $\\mathbf{G}$-modules and provide examples of generic direct summands for $\\mathbf{G}$ of type $\\mathrm{A}_1$ and $\\mathrm{A}_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-26T10:00:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G42",
      "17B55",
      "17B10"
    ],
    "keywords": [
      "generic direct summands",
      "tensor productsfor simple algebraic groups",
      "quantum group",
      "simple linear algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}