{
  "id": "1304.7490",
  "version": "v1",
  "published": "2013-04-28T17:18:22.000Z",
  "updated": "2013-04-28T17:18:22.000Z",
  "title": "A note on the structure theory of groups acting on the Bruhat Tits tree associated to $\\mathrm{PGL}_{2}(F)$",
  "authors": [
    "Inder Kaur"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note we prove the classical decomposition theorems for certain subgroups of the automorphism group of the Bruhat-Tits tree associated to $\\mathrm{PGL}_{2}(F)$, where $F$ is a local field. The results can be used to understand the representation theory of these subgroups. Moreover, we can also use the results to obtain similar decompositions for \\textit{any} closed transitive subgroup of the automorphism group of \\textit{any} Bruhat-Tits tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-28T17:18:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G25",
      "20E42"
    ],
    "keywords": [
      "bruhat tits tree",
      "structure theory",
      "groups acting",
      "bruhat-tits tree",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7490K"
    }
  }
}