{
  "id": "1501.02541",
  "version": "v1",
  "published": "2015-01-12T04:38:57.000Z",
  "updated": "2015-01-12T04:38:57.000Z",
  "title": "On equivariant principal bundles over wonderful compactifications",
  "authors": [
    "Indranil Biswas",
    "S. Senthamarai Kannan",
    "D. S. Nagaraj"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $G$ be a simple algebraic group of adjoint type over $\\mathbb C$, and let $M$ be the wonderful compactification of a symmetric space $G/H$. Take a $\\widetilde G$--equivariant principal $R$--bundle $E$ on $M$, where $R$ is a complex reductive algebraic group and $\\widetilde G$ is the universal cover of $G$. If the action of the isotropy group $\\widetilde H$ on the fiber of $E$ at the identity coset is irreducible, then we prove that $E$ is polystable with respect to any polarization on $M$. Further, for wonderful compactification of the quotient of $\\text{PSL}(n,{\\mathbb C})$, $n\\,\\neq\\, 4$ (respectively, $\\text{PSL}(2n,{\\mathbb C})$, $n \\geq 2$) by the normalizer of the projective orthogonal group (respectively, the projective symplectic group), we prove that the tangent bundle is stable with respect to any polarization on the wonderful compactification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-12T04:38:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q26",
      "14M27",
      "14M17"
    ],
    "keywords": [
      "wonderful compactification",
      "equivariant principal bundles",
      "simple algebraic group",
      "complex reductive algebraic group",
      "adjoint type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150102541B"
    }
  }
}