  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.
