{
  "id": "1902.02151",
  "version": "v1",
  "published": "2019-02-06T13:04:08.000Z",
  "updated": "2019-02-06T13:04:08.000Z",
  "title": "A note on certain Iwahori--Hecke modules of $GL_3$ in characteristic $p$",
  "authors": [
    "Peng Xu"
  ],
  "comment": "Preliminary version, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note, we show that the analogue of certain finiteness result of Barthel--Livn$\\acute{\\text{e}}$ on $GL_2$ fails for $GL_3$. More precisely, for the pro-$p$ Iwahori invariants of the maximal compact induction of $GL_3$ with trivial coefficient, we show there exist non-zero Iwahori--Hecke submodules of \\emph{infinite} codimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T13:04:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "iwahori-hecke modules",
      "characteristic",
      "maximal compact induction",
      "non-zero iwahori-hecke submodules",
      "finiteness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}