A partial Horn recursion in the cohomology of flag varieties

Abstract

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of "smaller" flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup product defined by Belkale and Kumar in \cite{BK06}. We also show that if a product of Schubert classes is non-vanishing on this deformation, then the associated structure constant can be written in terms of structure constants coming from induced Grassmannians.

arXiv commentv4: Final version, the current title has been changed from: "Horn recursion for a new product in the cohomology of partial flag varieties SLn/P" to appear in J. Alg. Comb., available through "online first"