A multiplicative formula for structure constants in the cohomology of flag varieties

Abstract

Let G be a complex semi-simple Lie group and let P,Q be a pair of parabolic subgroups of G such that Q contains P. Consider the flag varieties G/P, G/Q and Q/P. We show that certain structure constants in H^*(G/P) with respect to the Schubert basis can be written as a product of structure constants coming from H^*(G/Q) and H^*(Q/P) in a very natural way. The primary application is to compute Levi-movable structure constants defined by Belkale and Kumar. We also give a generalization of this product formula in the branching Schubert calculus setting.

arXiv commentFinal verison, 14 pages. The some of the results in this paper where independently obtained by N. Ressayre in arXiv:0812.2122. To appear in Mich. Math. Journal