{
  "id": "1302.5618",
  "version": "v3",
  "published": "2013-02-22T15:27:23.000Z",
  "updated": "2014-09-12T00:22:21.000Z",
  "title": "On Branching Rules of Depth-Zero Representations",
  "authors": [
    "Monica Nevins"
  ],
  "comment": "Final version: applications to bounds on GK-dimension added; deeper discussion conditions for coincidence of full branching rules of supercuspidals, final example corrected to include all three conjugacy classes of maximal tori",
  "journal": "Journal of Algebra 408 (2014) 1--27",
  "categories": [
    "math.RT"
  ],
  "abstract": "Using Bruhat-Tits theory, we analyse the restriction of depth-zero representations of a semisimple simply connected $p$-adic group $G$ to a maximal compact subgroup $K$. We prove the coincidence of branching rules within classes of Deligne-Lusztig supercuspidal representations. Furthermore, we show that under obvious compatibility conditions, the restriction to $K$ of a Deligne-Lusztig supercuspidal representation of $G$ intertwines with the restriction of a depth-zero principal series representation in infinitely many distinct components of arbitrarily large depth. Several qualitative and quantitative results are obtained, and their use is illustrated in an example.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-18T09:53:33.000Z",
      "abstract": "We present tools for analyzing the restriction of a smooth irreducible representation of a $p$-adic group $G$ to a maximal compact subgroup $K$, without recourse to case-by-case analysis. Using these, we prove the coincidence of branching rules of certain Deligne-Lusztig supercuspidal representations. Furthermore, we show that under mild compatibility conditions, the restriction to $K$ of a Deligne-Lusztig supercuspidal representation of $G$ intertwines with the restriction of a depth-zero principal series representation in infinitely many distinct components of arbitrarily large depth. We illustrate the results with examples.",
      "comment": "23 pages; large illustrative example added; submitted for publication. Comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-12T00:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05"
    ],
    "keywords": [
      "branching rules",
      "depth-zero representations",
      "deligne-lusztig supercuspidal representation",
      "depth-zero principal series representation",
      "maximal compact subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.5618N"
    }
  }
}