Schubert calculus and Gelfand-Zetlin polytopes

Abstract

We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope.

33 pages, 4 figures, introduction rewritten, Section 4 restructured, typos corrected

References in corpus (1)

• Gelfand-Zetlin polytopes and flag varieties

Cited by in corpus (7)

• Polytopes and large counterexamples
• Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers
• Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials)
• PBW filtration and monomial bases for Demazure modules in types A and C
• On the number of faces of Gelfand-Zetlin polytopes
• Hybrid Pipe Dreams for Key Polynomials
• The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope