Tensor products and Minkowski sums of Mirkovic-Vilonen polytopes

Abstract

The purpose of this paper is to prove that the Mirkovic-Vilonen (MV for short) polytope corresponding to the tensor product of two arbitrary MV polytopes is contained in the Minkowski sum of these two MV polytopes. This generalizes the result in our previous paper [KNS], which was obtained under the assumption that the first tensor factor is an extremal MV polytope.