Schubert calculus and Gelfand-Zetlin polytopes
Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
TL;DR
This paper introduces a novel geometric method for Schubert calculus on flag varieties by utilizing Gelfand-Zetlin polytopes and their volume polynomials to compute intersection products.
Contribution
It presents a new approach that connects Schubert calculus with polytope face intersections, enabling computations via volume polynomials of Gelfand-Zetlin polytopes.
Findings
Intersection products computed through face intersections of Gelfand-Zetlin polytopes
Volume polynomial associated with these polytopes encodes Schubert calculus data
New geometric perspective on Schubert calculus using 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.