{
  "id": "2209.09748",
  "version": "v1",
  "published": "2022-09-20T14:28:47.000Z",
  "updated": "2022-09-20T14:28:47.000Z",
  "title": "Minimal parabolic subgroups and automorphism groups of Schubert varieties",
  "authors": [
    "S. Senthamarai Kannan",
    "Pinakinath Saha"
  ],
  "comment": "To appear in Journal of Lie Theory, 28 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $G$ be a simple simply-laced algebraic group of adjoint type over the field $\\mathbb{C}$ of complex numbers, $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G.$ In this article, we show that $\\omega_\\alpha$ is a minuscule fundamental weight if and only if for any parabolic subgroup $Q$ containing $B$ properly, there is no Schubert variety $X_{Q}(w)$ in $G/Q$ such that the minimal parabolic subgroup $P_{\\alpha}$ of $G$ is the connected component, containing the identity automorphism of the group of all algebraic automorphisms of $X_{Q}(w).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-20T14:28:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "14M17"
    ],
    "keywords": [
      "minimal parabolic subgroup",
      "schubert variety",
      "automorphism groups",
      "simple simply-laced algebraic group",
      "minuscule fundamental weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}