Koppelman formulas on flag manifolds and harmonic forms
Artikel i vetenskaplig tidskrift, 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

Författare

Håkan Samuelsson Kalm

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Henrik Seppänen

Universität Paderborn

Mathematische Zeitschrift

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

Vol. 272 1087-1095

Ämneskategorier

Matematik

DOI

10.1007/s00209-011-0976-6