{
  "id": "1305.2638",
  "version": "v3",
  "published": "2013-05-12T21:43:02.000Z",
  "updated": "2014-03-07T14:43:40.000Z",
  "title": "The local Langlands correspondence for inner forms of $SL_n$",
  "authors": [
    "Anne-Marie Aubert",
    "Paul Baum",
    "Roger Plymen",
    "Maarten Solleveld"
  ],
  "comment": "In the second version Theorem 5.3 was restricted to n' = n-1 and the proof was modified accordingly. Also references to the work of Ganapathy were added. It turned out that the proof of Theorem 4.4 in versions 1 and 2 was incorrect and beyond repair, so we removed this result in version 3. Consequently Theorems 4.4 and 6.1 (from v1 and v2) only remain valid with worse lower bounds",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for $SL_n (F)$ enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of $SL_n (F)$. An analogous result is shown in the archimedean case. To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of $GL_n (F)$, when the fields are close enough compared to the depth of the representations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-07T14:43:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "22E50"
    ],
    "keywords": [
      "local langlands correspondence",
      "inner forms",
      "non-archimedean local field",
      "conjugacy classes",
      "langlands parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2638A"
    }
  }
}