On equivariant principal bundles over wonderful compactifications
Indranil Biswas, S. Senthamarai Kannan, D. S. Nagaraj

TL;DR
This paper proves polystability of certain equivariant principal bundles and stability of tangent bundles over wonderful compactifications of symmetric spaces, extending understanding of geometric structures on these spaces.
Contribution
It establishes conditions under which equivariant principal bundles are polystable and shows tangent bundle stability for specific wonderful compactifications.
Findings
Equivariant principal bundles with irreducible isotropy action are polystable.
Tangent bundles of certain wonderful compactifications are stable.
Results apply to compactifications of quotients of PSL(n,C) by specific subgroups.
Abstract
Let be a simple algebraic group of adjoint type over , and let be the wonderful compactification of a symmetric space . Take a --equivariant principal --bundle on , where is a complex reductive algebraic group and is the universal cover of . If the action of the isotropy group on the fiber of at the identity coset is irreducible, then we prove that is polystable with respect to any polarization on . Further, for wonderful compactification of the quotient of , (respectively, , ) 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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds
