13 citations · 28 across the 4 of their papers we have counts for
4 papers
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…
Mirkovic-Vilonen cycles and polytopes
Joel Kamnitzer
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 t…
The octahedron recurrence and gl(n) crystals
Andre Henriques, Joel Kamnitzer
We study the hive model of gl(n) tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the ass…
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…