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

SPEAKER: Edward Richmond

TITLE: A multiplicative formula for structure coefficients 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 P. Belkale and S. Kumar. We also give a generalization of this result to the “branching Schubert calculus” setting. Note that the results of this talk are a work in progress.