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 | References | Similar Articles | Additional Information

Abstract: Let be a generic coadjoint orbit of a compact semi-simple Lie group . Weight varieties are the symplectic reductions of by the maximal torus in . 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 , and it makes explicit the dependence on and a parameter in .

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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

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