{
  "id": "1012.5548",
  "version": "v1",
  "published": "2010-12-26T23:15:11.000Z",
  "updated": "2010-12-26T23:15:11.000Z",
  "title": "Supercuspidal characters of $\\operatorname{SL}_2$ over a $p$-adic field",
  "authors": [
    "Jeffrey D. Adler",
    "Stephen DeBacker",
    "Paul J. Sally, Jr.",
    "Loren Spice"
  ],
  "comment": "51 pages; 1 figure; to appear in \"Harmonic analysis on reductive, p-adic groups\"",
  "categories": [
    "math.RT"
  ],
  "abstract": "The character formulas of Sally and Shalika are an early triumph in $p$-adic harmonic analysis, but, to date, the calculations underlying the formulas have not been available. In this paper, which should be viewed as a precursor of the forthcoming volume by the authors and Alan Roche, we leverage modern technology (for example, the Moy-Prasad theory) to compute explicit character tables. An interesting highlight is the computation of the 'exceptional' supercuspidal characters, i.e., those depth-zero representations not arising by inflation-induction from a Deligne-Lusztig representation of finite $\\operatorname{SL}_2$; this provides a concrete application for the recent work of DeBacker and Kazhdan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-26T23:15:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E35",
      "22E50",
      "20G05"
    ],
    "keywords": [
      "supercuspidal characters",
      "adic field",
      "adic harmonic analysis",
      "explicit character tables",
      "concrete application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5548A"
    }
  }
}