On the f-vectors of Gelfand-Cetlin polytopes

Abstract

A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating function of f-vectors of GC-polytopes. This solves the open problem (2) posed by Gusev, Kritchenko, and Timorin in [GKT].

14 pages

Cited by in corpus (12)

• Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
• Immersed two-spheres and SYZ with Application to Grassmannians
• Lagrangian fibers of Gelfand-Cetlin systems
• Monotone Lagrangians in flag varieties
• Fukaya category of Grassmannians: rectangles
• On the combinatorics of string polytopes
• Diameter and Automorphisms of Gelfand-Tsetlin Polytopes
• Lagrangian fibers of Gelfand--Cetlin systems of $\mathrm{SO}(n)$-type
• A Leray-Serre spectral sequence for Lagrangian Floer theory
• A metric on the moduli space of bodies
• Local normal forms for multiplicity free $U(n)$ actions on coadjoint orbits
• On the number of faces of Gelfand-Zetlin polytopes