Koppelman formulas on flag manifolds

Details Koppelman formulas on flag manifolds Koppelman formulas on flag manifolds

2010-03-29

arxiv.org/abs/1003.5646v2

Mathematics

Complex Variables

Scientific paper

We construct Koppelman formulas on manifolds of flags in $\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.

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