On combinatorics of string polytopes in types B and C

IF 1 3区 数学 Q1 MATHEMATICS
Yunhyung Cho , Naoki Fujita , Eunjeong Lee
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引用次数: 0

Abstract

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.
B型和C型弦多面体的组合学
弦多面体是一种有理凸多面体,其晶格点参数化了由弦锥根据最高权值的显式仿射不等式得到的最高权值晶体基。它还继承了一个标志品种的几何信息,如环退化,牛顿-奥肯科夫体,镜像对称,舒伯特微积分,等等。本文研究了B型和C型弦多面体的组合性质,给出了B型和C型弦多面体的显式描述,类似于a型弦锥体的Gleizer-Postnikov描述。作为应用,我们刻画了C型弦多面体在特定的最高权下与C型的Gelfand-Tsetlin多面体单模等价的特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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