2023/06/20 by Cho, Yunhyung, Fujita, Naoki, Lee, Eunjeong
#14M15 #52B20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05E10 #Representation Theory (math.RT) #secondary: 05A05
paper · doi:10.48550/arxiv.2306.11242
A string polytope is a rational convex polytope whose lattice points parametrize a highest weight crystal basis, which is obtained from a string cone by explicit affine inequalities depending on a highest weight. It also inherits geometric information of a flag variety such as toric degenerations, Newton-Okounkov bodies, mirror symmetry, Schubert calculus, and so on. In this paper, we study combinatorial properties of string polytopes in types B and C by giving an explicit description of string cones in these types which is analogous to Gleizer-Postnikov's description of string cones in type A. As an application, we characterize string polytopes in type C which are unimodularly equivalent to the Gelfand-Tsetlin polytope in type C for a specific highest weight.