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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 symplectic reductions of generic coadjoint orbits


Authors: R. F. Goldin and A.-L. Mare
Journal: Proc. Amer. Math. Soc. 132 (2004), 3069-3074
MSC (2000): Primary 53D20, 14M15
Published electronically: June 2, 2004
MathSciNet review: 2063128
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Abstract: Let $\mathcal{O}_\lambda$ be a generic coadjoint orbit of a compact semi-simple Lie group $K$. Weight varieties are the symplectic reductions of $\mathcal{O}_\lambda$ by the maximal torus $T$ in $K$. We use a theorem of Tolman and Weitsman to compute the cohomology ring of these varieties. Our formula relies on a Schubert basis of the equivariant cohomology of $\mathcal{O}_\lambda$, and it makes explicit the dependence on $\lambda$ and a parameter in $Lie(T)^*=:\mathfrak{t}^*$.


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Additional Information

R. F. Goldin
Affiliation: Mathematical Sciences, George Mason University, MS 3F2, 4400 University Dr., Fairfax, Virginia 22030
Email: rgoldin@gmu.edu

A.-L. Mare
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: amare@math.toronto.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07443-X
PII: S 0002-9939(04)07443-X
Keywords: Coadjoint orbits, symplectic reduction, Schubert classes
Received by editor(s): November 8, 2002
Published electronically: June 2, 2004
Additional Notes: The first author was supported by NSF-DMS grant number 0305128
Communicated by: Rebecca Herb
Article copyright: © Copyright 2004 American Mathematical Society