Journal of Lie Theory 33 (2023), No. 3, 719--746
Copyright Heldermann Verlag 2023
Mirkovic-Vilonen Polytopes and Masures
Tristan Bozec
IMAG UMR 5149, Université de Montpellier, France
tristan.bozec@umontpellier.fr
Stéphane Gaussent
Institut Camille Jordan UMR 5208, Université Jean Monnet, Saint-Etienne, France
stephane.gaussent@univ-st-etienne.fr
In the framework of masures, we relate the affine Mirkovic-Vilonen polytopes defined by Baumann, Kamnitzer and Tingley in 2014 to Littelmann path model. Thanks to the retractions sending the masure onto the standard apartment, we recover the bottom part of the affine MV polytope. We are also able to read on the paths the partitions decorating these polytopes in the case of affine sl2.
Keywords: Kac-Moody groups, masures, Littelmann path model, affine Mirkovic-Vilonen polytopes.
MSC: 20G44, 20E42, 05E10.
[ Fulltext-pdf (229 KB)] for subscribers only.