On the combinatorics of string polytopes

2019/03/30 by Yunhyung Cho, Yoosik Kim, Cho, Yunhyung +5
Mathematics · #52B12 14M15 20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1904.00130

openalex publication_date 2019/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a reduced word \bf i of the longest element in the Weyl group of SL_n+1(ℂ), one can associate the string cone C_{\bf i} which parametrizes the dual canonical bases. In this paper, we classify all \bf i's such that C_{\bf i} is simplicial. We also prove that for any regular dominant weight λ of \mathfraksl_n+1(ℂ), the corresponding string polytope Δ_{\bf i}(λ) is unimodularly equivalent to the Gelfand-Cetlin polytope associated to λ if and only if C_{\bf i} is simplicial. Thus we completely characterize Gelfand-Cetlin type string polytopes in terms of \bf i.

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