Geodesic
Mirkovic-Vilonen Polytopes and Masures
Tristan Bozec1 ; Stéphane Gaussent2
1IMAG UMR 5149, Université de Montpellier, France
2Institut Camille Jordan UMR 5208, Université Jean Monnet, Saint-Etienne, France
Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 719-746

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 20G44, 20E42, 05E10
Mots-clés : Kac-Moody groups, masures, Littelmann path model, affine Mirkovic-Vilonen polytopes

Tristan Bozec  1   ; Stéphane Gaussent  2

1 IMAG UMR 5149, Université de Montpellier, France
2 Institut Camille Jordan UMR 5208, Université Jean Monnet, Saint-Etienne, France 
Tristan Bozec; Stéphane Gaussent. Mirkovic-Vilonen Polytopes and Masures. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 719-746. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a2/
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     title = {Mirkovic-Vilonen {Polytopes} and {Masures}},
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