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Transformation formulas in quantum cohomology

Published online by Cambridge University Press:  04 December 2007

Prakash Belkale
Prakash Belkale
Affiliation:
Department of Mathematics, UNC-Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, NC 27599, USAbelkale@email.unc.edu
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Abstract

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We discuss a natural action of the center of G on the Gromov–Witten numbers of G/B's and G/P's. This action is suggested by some problems in representation theory. The quantum Schubert calculus of Grassmannians is an easy consequence of this action. We also strengthen a theorem of Fulton and Woodward, in the case of Grasmannians.

Keywords

Grassmann varietycohomologyparabolic subgroup14N15 (primary)14N35 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 778 - 792
Copyright
Foundation Compositio Mathematica 2004