{
  "id": "2008.10999",
  "version": "v1",
  "published": "2020-08-25T13:38:50.000Z",
  "updated": "2020-08-25T13:38:50.000Z",
  "title": "On Ext-Quivers of Blocks of Weight Two for Symmetric Groups",
  "authors": [
    "Susanne Danz",
    "Karin Erdmann"
  ],
  "comment": "47 pages (of this, 17 pages is an appendix)",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we investigate blocks of symmetric groups of weight 2 over fields of odd characteristic $p$. We develop an algorithm that relates the quivers of two such blocks forming a $(2:1)$ pair, as introduced by Scopes. We then apply the algorithm to blocks whose $p$-cores are hook partitions, in order to explicitly determine the quivers of these blocks. As a consequence we conclude that two $p$-blocks $B_1$ and $B_2$ of symmetric groups of weight $2$ whose $p$-cores are hook partitions are Morita equivalent if and only if $B_2$ or its conjugate block is in the same Scopes class as $B_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-25T13:38:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "29C20",
      "20C30",
      "16D90"
    ],
    "keywords": [
      "symmetric groups",
      "ext-quivers",
      "hook partitions",
      "conjugate block",
      "odd characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}