Polytopal Estimate of Mirkovic-Vilonen polytopes lying in a Demazure crystal

2009/12/03 by Syu Kato, Kato, Syu, Satoshi Naito +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Analytic and geometric function theory #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.0912.0586

openalex publication_date 2009/12/03 · arxiv created 2009/12/24 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a polytopal estimate of Mirković-Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirković-Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirković-Vilonen polytope to lie in a Demazure crystal.

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