Deformed Cohomology of Flag Varieties
Oliver Pechenik, Dominic Searles
TL;DR
This paper develops a two-parameter deformation of flag variety cohomology, providing a new, simpler proof for the well-definedness of the Belkale-Kumar product and exploring special cases with geometric significance.
Contribution
It introduces a novel two-parameter deformation framework for flag variety cohomology, unifying and simplifying previous results, including the Belkale-Kumar product.
Findings
New deformation of cohomology with two parameters
Simplified proof of the Belkale-Kumar product's well-definedness
Identification of special cases with geometric applications
Abstract
This paper introduces a two-parameter deformation of the cohomology of generalized flag varieties. One special case is the Belkale-Kumar deformation (used to study eigencones of Lie groups). Another picks out intersections of Schubert varieties that behave nicely under projections. Our construction yields a new proof that the Belkale-Kumar product is well-defined. This proof is shorter and more elementary than earlier proofs.
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