{
  "id": "1610.02645",
  "version": "v1",
  "published": "2016-10-09T08:47:57.000Z",
  "updated": "2016-10-09T08:47:57.000Z",
  "title": "On $L$-packets and depth for $SL_2(K)$ and its inner form",
  "authors": [
    "Anne-Marie Aubert",
    "Sergio Mendes",
    "Roger Plymen",
    "Maarten Solleveld"
  ],
  "comment": "22 pages. This article supercedes arXiv:1402.0184 and arXiv:1302.6038",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame. We also work out a classification of all $L$-packets for $SL_2 (K)$ and for its non-split inner form, and we provide explicit formulae for the depths of their $L$-parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-09T08:47:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G25"
    ],
    "keywords": [
      "local non-archimedean field",
      "non-split inner form",
      "corresponding langlands parameter",
      "explicit formulae",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}