How do we compute the sheaf cohomology of the universal subbundle and universal quotient bundle of the Grassmannian $G(k,V)$?



Sheaf cohomology of the universal sub and quotient bundles of the Grassmannian
See them as pushforwards of line bundles from the flag manifold by using
Borel-Weil fiberwise. Then use Borel-Weil up on the flag manifold.
Jerzy Weyman's book is the source I know of for these techniques.


