Transformation Groups

, Volume 17, Issue 1, pp 195–207

Tensor products and Minkowski sums of Mirković–Vilonen polytopes


DOI: 10.1007/s00031-011-9159-0

Cite this article as:
Kato, S., Naito, S. & Sagaki, D. Transformation Groups (2012) 17: 195. doi:10.1007/s00031-011-9159-0


The purpose of this paper is to prove that the Mirković–Vilonen (MV) polytope corresponding to the tensor product of two arbitrary MV polytopes is contained, as a set, in the Minkowski sum of these two MV polytopes. This result generalizes the one in our previous paper, which was obtained under the assumption that the first tensor factor is an extremal MV polytope.

AMS classification

Primary, 17B37, 20G05Secondary, 17B10, 14M15, 05E15

Key words and phrases

Crystal basistensor productMirković–Vilonen cycleMirković–Vilonen polytopeMinkowski sum

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Institute of MathematicsUniversity of TsukubaTsukuba, IbarakiJapan