Mirkovic-vilonen Cycles and Polytopes
نویسنده
چکیده
We give an explicit description of the Mirkovic-Vilonen cycles on the affine Grassmannian for arbitrary 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 every 2-face of it is a rank 2 MV polytope.
منابع مشابه
The Crystal Structure on the Set of Mirković-vilonen Polytopes
In an earlier work, we proved that MV polytopes parameterize both Lusztig’s canonical basis and the Mirković-Vilonen cycles on the Affine Grassmannian. Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles side). We show that these two crystal structures agree. As an application, we consider a ...
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