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Cohomology of line bundles on the cotangent bundle of a Grassmannian
Author(s):
Eric
N.
Sommers
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3291-3296.
MSC (2000):
Primary 20G10;
Secondary 14F05
Posted:
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  have cohomology groups isomorphic to those of a line bundle on the cotangent bundle of the dual Grassmannian arising from the dominant character  , where  is the longest element of the Weyl group of  .
References:
-
- 1.
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- 2.
- M. Demazure, A very simple proof of Bott's Theorem, Invent. Math. 33 (1976), 271-272. MR 0414569 (54:2670)
- 3.
- J. C. Jantzen, Nilpotent orbits in representation theory, Lie theory, Progr. Math., 228, Birkhäuser, Boston, 2004, pp. 1-211. MR 2042689 (2005c:14055)
- 4.
- E. Sommers, Normality of nilpotent varieties in
 , J. Algebra 270 (2003), no. 1, 288-306. MR 2016663 (2004i:20085) - 5.
- -, Normality of very even nilpotent varieties in
 , Bull. London Math. Soc. 37 (2005), no. 3, 351-360. MR 2131388 (2005k:20116) - 6.
- J. F. Thomsen, Normality of certain nilpotent varieties in positive characteristic, J. Algebra 227 (2000), 595-613. MR 1759837 (2001g:14079)
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Additional Information:
Eric
N.
Sommers
Affiliation:
University of Massachusetts-Amherst, Amherst, Massachusetts 01003
Email:
esommers@math.umass.edu
DOI:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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