{
  "id": "2208.05711",
  "version": "v1",
  "published": "2022-08-11T09:17:49.000Z",
  "updated": "2022-08-11T09:17:49.000Z",
  "title": "Schurian-finiteness of blocks of type $A$ Hecke algebras II",
  "authors": [
    "Sinéad Lyle",
    "Liron Speyer"
  ],
  "comment": "11 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "For any algebra $A$ over an algebraically closed field $\\mathbb{F}$, we say that an $A$-module $M$ is Schurian if $\\mathrm{End}_A(M) \\cong \\mathbb{F}$. We say that $A$ is Schurian-finite if there are only finitely many isomorphism classes of Schurian $A$-modules, and Schurian-infinite otherwise. In this paper, we build on the work of Ariki and the second author to show that all blocks of type $A$ Hecke algebras of weight at least $2$ in quantum characteristic $e \\geq 3$ are Schurian-infinite. This proves that if $e \\geq 3$ then blocks of type $A$ Hecke algebras are Schurian-finite if and only if they are representation-finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-11T09:17:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "16G10"
    ],
    "keywords": [
      "hecke algebras",
      "schurian-finiteness",
      "quantum characteristic",
      "isomorphism classes",
      "schurian-infinite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}