Mirkovic-Vilonen cycles and polytopes

Details Mirkovic-Vilonen cycles and polytopes Mirkovic-Vilonen cycles and polytopes

2005-01-22

arxiv.org/abs/math/0501365v2

Mathematics

Algebraic Geometry

42 pages, v2: new sections added, references improved, mistakes corrected, exposition improved

Scientific paper

We give an explicit description of the Mirkovic-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 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.

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