Koppelman formulas on flag manifolds and harmonic forms
Journal article, 2012

We construct Koppelman formulas on manifolds of flags in 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 -equation. We also construct reproducing kernels for harmonic (p, q)-forms in the case of Grassmannians.

Integral formula

Flag manifold

Holomorphic vector bundle

Lie group

Author

Håkan Samuelsson Kalm

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Henrik Seppänen

Padernborn University

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 272 3-4 1087-1095

Subject Categories

Mathematics

DOI

10.1007/s00209-011-0976-6

More information

Latest update

3/19/2018