Cohomology of line bundles on the cotangent bundle of a Grassmannian

Sommers, Eric

doi:10.1090/S0002-9939-09-09936-5

Cohomology of line bundles on the cotangent bundle of a Grassmannian
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by Eric N. Sommers PDF

Proc. Amer. Math. Soc. 137 (2009), 3291-3296 Request permission

Abstract:

We show that certain line bundles on the cotangent bundle of a Grassmannian arising from an anti-dominant character $\lambda$ have cohomology groups isomorphic to those of a line bundle on the cotangent bundle of the dual Grassmannian arising from the dominant character $w_0(\lambda )$, where $w_0$ is the longest element of the Weyl group of $SL_{l+1}(k)$.

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