Homogeneous Vector Bundles

  title={Homogeneous Vector Bundles},
  author={Raoul Bott},
  journal={Annals of Mathematics},
  • R. Bott
  • Published 1 September 1957
  • Mathematics
  • Annals of Mathematics

The cohomology of left-invariant elliptic involutive structures on compact Lie groups

Inspired by the work of Chevalley and Eilenberg on the de Rham cohomology on compact Lie groups, we prove that, under certain algebraic and topological conditions, the cohomology associated to


Let b be a Borel subalgebra of the symplectic Lie algebra sp(2n, C) and let n be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of b and the

Fe b 20 04 Principal Series Representations of Direct Limit Groups

We combine the geometric realization of principal series representations of [28] with the Bott–Borel–Weil Theorem for direct limits of compact groups found in [22], obtaining limits of principal

A Bott-Borel-Weil theory for direct limits of algebraic groups

<abstract abstract-type="TeX"><p>We develop a Bott-Borel-Weil theory for direct limits of algebraic groups. Some of our results apply to locally reductive ind-groups <i>G</i> in general, i.e., to

Equivariant holomorphic Morse inequalities. II. Torus and non-abelian group actions

We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity

The nondegeneration of the Hodge-de Rham spectral sequence

Using an integrable, homogeneous complex structure on the compact group SO(9), we show that the Hodge-de Rham spectral sequence for this non-Kahler compact complex manifold does not degenerate at Ei,

On hypersurfaces of a complex Grassmann manifold

Polarized K 3 surfaces of genus 18 and 20

A surface, i.e., 2-dimensional compact complex manifold, S is of type K3 if its canonical line bundleOS(KS) is trivial and if H(S,OS) = 0. An ample line bundle L on a K3 surface S is a polarization

On the rigidity of super-Grassmannians

The rigidity of the complex super-Grassmannian Grm|n,k|l with 0<k<m, 0<l<n, supposing that (k, l) ≠ (1,n−1), (m−1, 1), (1,n−2), (m−2, 1), (2,n−1), (m−1, 2), is proved.

Théorèmes d'annulation pour les fibrés associés à un fibré ample

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