Tensor products and Minkowski sums of Mirkovic-Vilonen polytopes

TL;DR

This paper proves that the MV polytope of a tensor product of two MV polytopes is contained within their Minkowski sum, extending previous results to arbitrary MV polytopes without restrictions.

Contribution

It generalizes earlier work by showing the inclusion for tensor products of any MV polytopes, not just extremal cases.

Findings

MV polytope of tensor product is contained in Minkowski sum

Generalization of previous extremal case result

Extends understanding of MV polytope operations

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.