2021/04/20 by Naoki Fujita, Fujita, Naoki
Mathematics · #06A07 #14M15 #52B20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary 14M25 #Representation Theory (math.RT) #Secondary 05E10
paper · pdf · doi:10.48550/arxiv.2104.09929
openalex publication_date 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Marked chain-order polytopes are convex polytopes constructed from a marked poset, which give a discrete family relating a marked order polytope with a marked chain polytope. In this paper, we consider the Gelfand-Tsetlin poset of type A, and realize the associated marked chain-order polytopes as Newton-Okounkov bodies of the flag variety. Our realization connects previous realizations of Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg polytopes as Newton-Okounkov bodies in a uniform way. As an application, we prove that the flag variety degenerates into the irreducible normal projective toric variety corresponding to a marked chain-order polytope. We also construct a specific basis of an irreducible highest weight representation which is naturally parametrized by the set of lattice points in a marked chain-order polytope.