{
  "id": "1210.3268",
  "version": "v1",
  "published": "2012-10-11T15:21:45.000Z",
  "updated": "2012-10-11T15:21:45.000Z",
  "title": "A new realization of the Langlands correspondence for PGL(2,F)",
  "authors": [
    "Moshe Adrian"
  ],
  "comment": "Accepted to Journal of Number Theory. 30 pages. Most of this work is contained in the paper \"A New Construction for the Tame Local Langlands Correspondence for GL(n,F), n a prime\" arXiv:1008.2727",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic tori. Taking a cue from real groups, we propose that supercuspidal representations are naturally parameterized by characters of covers of tori. Over the reals, Harish-Chandra defined the discrete series representations by specifying their characters restricted to an elliptic torus, and these characters may naturally be expressed in terms of characters of a cover of the torus. We write down a natural analogue of Harish-Chandra's character for PGL(2,F), and show that it is the character of a unique supercuspidal representation, on a canonical subset of the elliptic torus. This paves the way for a realization of the local Langlands correspondence for PGL(2,F) that eliminates the need for any character twists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-11T15:21:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S37",
      "22E50"
    ],
    "keywords": [
      "local langlands correspondence",
      "realization",
      "elliptic torus",
      "discrete series representations",
      "odd residual characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3268A"
    }
  }
}