Polytopal Estimate of Mirkovic-Vilonen polytopes lying in a Demazure crystal
Syu Kato, Satoshi Naito, and Daisuke Sagaki
TL;DR
This paper introduces a polytopal estimate method for Mirković-Vilonen polytopes within Demazure crystals, using Minkowski sums, and offers a necessary condition for such polytopes to belong to Demazure crystals.
Contribution
It provides a novel polytopal estimate approach for Mirković-Vilonen polytopes in Demazure crystals based on Minkowski sums, advancing understanding of their structure.
Findings
Polytopal estimate of Mirković-Vilonen polytopes in Demazure crystals
Necessary polytopal condition for polytopes to lie in Demazure crystals
Connection between Minkowski sums and crystal structure
Abstract
In this paper, we give a polytopal estimate of Mirkovi\'c-Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi\'c-Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi\'c-Vilonen polytope to lie in a Demazure crystal.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Analytic and geometric function theory · Mathematical functions and polynomials