%0 Journal Article
%T Polytopal Estimate of Mirkovic-Vilonen polytopes lying in a Demazure crystal
%A Syu Kato
%A Satoshi Naito
%A Daisuke Sagaki
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0912.0586v2