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Koppelman formulas on flag manifolds and harmonic forms

Håkan Samuelsson (Institutionen för matematiska vetenskaper, matematik) ; Henrik Seppänen
Mathematische Zeitschrift (0025-5874). Vol. 272 (2012), 3-4, p. 1087-1095.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Integral formula, Holomorphic vector bundle, Flag manifold, Lie group



Denna post skapades 2012-12-13. Senast ändrad 2012-12-13.
CPL Pubid: 167667

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematikInstitutionen för matematiska vetenskaper, matematik (GU)

Ämnesområden

Matematik