{"title":"On combinatorics of string polytopes in types B and C","authors":"Yunhyung Cho , Naoki Fujita , Eunjeong Lee","doi":"10.1016/j.ejc.2025.104126","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mi>B</mi></math></span> and <span><math><mi>C</mi></math></span> by giving an explicit description of string cones in these types which is analogous to Gleizer–Postnikov’s description of string cones in type <span><math><mi>A</mi></math></span>. As an application, we characterize string polytopes in type <span><math><mi>C</mi></math></span> which are unimodularly equivalent to the Gelfand–Tsetlin polytope in type <span><math><mi>C</mi></math></span> for a specific highest weight.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"126 ","pages":"Article 104126"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669825000083","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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 and by giving an explicit description of string cones in these types which is analogous to Gleizer–Postnikov’s description of string cones in type . As an application, we characterize string polytopes in type which are unimodularly equivalent to the Gelfand–Tsetlin polytope in type for a specific highest weight.
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.