{
  "id": "0710.3146",
  "version": "v1",
  "published": "2007-10-16T18:16:36.000Z",
  "updated": "2007-10-16T18:16:36.000Z",
  "title": "Cuspidal representations which are not strongly cuspidal",
  "authors": [
    "Alexander Stasinski"
  ],
  "comment": "5 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a description of all the cuspidal representations of $\\mathrm{GL}_4(\\mathfrak{o}_2)$, where $\\mathfrak{o}_2$ is a finite ring coming from the ring of integers in a local field, modulo the square of its maximal ideal $\\mathfrak{p}$. This shows in particular the existence of representations which are cuspidal, yet are not strongly cuspidal, that is, do not have orbit with irreducible characteristic polynomial mod $\\mathfrak{p}$. It has been shown by Aubert, Onn, and Prasad that this phenomenon cannot occur for $\\mathrm{GL}_n$, when $n$ is prime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-16T18:16:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cuspidal representations",
      "strongly cuspidal",
      "irreducible characteristic polynomial mod",
      "local field",
      "maximal ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3146S"
    }
  }
}