13 citations · 28 across the 4 of their papers we have counts for
5 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…
Central Binomial Sums, Multiple Clausen Values and Zeta Values
J. M. Borwein, D. J. Broadhurst, J. Kamnitzer
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alte…