Geodesic
Mirkovic-Vilonen Polytopes and Masures
Journal of Lie theory, Tome 33 (2023) no. 3, pp. 719-746
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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 
@article{JLT_2023_33_3_JLT_2023_33_3_a2,
     author = {T. Bozec and S. Gaussent},
     title = {Mirkovic-Vilonen {Polytopes} and {Masures}},
     journal = {Journal of Lie theory},
     pages = {719--746},
     year = {2023},
     volume = {33},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2023_33_3_JLT_2023_33_3_a2/}
}
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T. Bozec; S. Gaussent. Mirkovic-Vilonen Polytopes and Masures. Journal of Lie theory, Tome 33 (2023) no. 3, pp. 719-746. http://geodesic.mathdoc.fr/item/JLT_2023_33_3_JLT_2023_33_3_a2/