{
  "id": "1702.08364",
  "version": "v1",
  "published": "2017-02-27T16:42:53.000Z",
  "updated": "2017-02-27T16:42:53.000Z",
  "title": "The full automorphism group of $\\overline{T}$",
  "authors": [
    "Indranil Biswas",
    "Subramaniam Senthamarai Kannan",
    "Donihakalu Shankar Nagaraj"
  ],
  "comment": "Final version",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $\\overline G$ be the wonderful compactification of a simple affine algebraic group $G$ of adjoint type defined over $\\mathbb C.$ Let ${\\overline T}\\subset \\overline G$ be the closure of a maximal torus $T\\subset G.$ We prove that the group of all automorphisms of the variety $\\overline T$ is the semi-direct product $N_G(T)\\rtimes D,$ where $N_G(T)$ is the normalizer of $T$ in $G$ and $D$ is the group of all automorphisms of the Dynkin diagram, if $G\\not= {\\rm PSL}(2,\\mathbb{C})$. Note that if $G = {\\rm PSL}(2,\\mathbb{C})$, then $\\overline{T} = {\\mathbb C}{\\mathbb P}^1$ and so in this case $\\text{Aut}(\\overline T)= {\\rm PSL}(2,\\mathbb{C})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-27T16:42:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L10",
      "14L30"
    ],
    "keywords": [
      "full automorphism group",
      "simple affine algebraic group",
      "dynkin diagram",
      "adjoint type",
      "maximal torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}