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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cohomology of line bundles on the cotangent bundle of a Grassmannian


Author: Eric N. Sommers
Journal: Proc. Amer. Math. Soc. 137 (2009), 3291-3296
MSC (2000): Primary 20G10; Secondary 14F05
Published electronically: June 5, 2009
MathSciNet review: 2515398
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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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Additional Information

Eric N. Sommers
Affiliation: University of Massachusetts-Amherst, Amherst, Massachusetts 01003
Email: esommers@math.umass.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09936-5
PII: S 0002-9939(09)09936-5
Received by editor(s): June 17, 2008
Received by editor(s) in revised form: February 19, 2009
Published electronically: June 5, 2009
Additional Notes: The author was supported in part by NSF grant DMS-0201826
Dedicated: To Professor Shoji on the occasion of his 60th birthday
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.