2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140837We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As a consequence we obtain some vanishing theorems of the Bott-Borel-Weil type. We also relate the projection part of our formulas to the Bergman kernels associated to the line bundles.sections 5.3 and 6.2 are newComplex VariablesRepresentation Theory32A26; 32L10; 32M10; 32M05text