Geodesic
Mirković-Vilonen cycles and polytopes
Joel Kamnitzer1
1 Department of Mathematics, University of Toronto, Room 6290, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
Annals of mathematics, Tome 171 (2010) no. 1, pp. 245-294.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We give an explicit description of the Mirković-Vilonen cycles on the affine Grassmannian for arbitrary complex reductive groups. We also give a combinatorial characterization of the MV polytopes. We prove that a polytope is an MV polytope if and only if it is a lattice polytope whose defining hyperplanes are parallel to those of the Weyl polytopes and whose 2-faces are rank 2 MV polytopes. As an application, we give a bijection between Lusztig’s canonical basis and the set of MV polytopes.
DOI : 10.4007/annals.2010.171.245

Joel Kamnitzer 1

1 Department of Mathematics, University of Toronto, Room 6290, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4 
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Joel Kamnitzer. Mirković-Vilonen cycles and polytopes. Annals of mathematics, Tome 171 (2010) no. 1, pp. 245-294. doi : 10.4007/annals.2010.171.245. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.245/

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