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math.QA2005★ 3 cited
The crystal structure on the set of Mirkovic-Vilonen polytopes
Joel Kamnitzer
In an earlier work, we proved that MV polytopes parameterize both Lusztig's canonical basis and the Mirkovic-Vilonen cycles on the Affine Grassmannian. Each of these sets has a cry…
math.QA2004★ 1 cited
Crystals and coboundary categories
Andre Henriques, Joel Kamnitzer
Following an idea of A. Berenstein, we define a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that this endows the category o…