114 citations · 500 across the 43 of their papers we have counts for
7 papers · 1 filter
Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]
Joel Kamnitzer
Given a vector space with an action of a semi-simple Lie algebra, we can try to "categorify" this representation, which means finding a category where the generators of the Lie alg…
Buildings, spiders, and geometric Satake
Bruce Fontaine, Joel Kamnitzer, Greg Kuperberg
Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we constru…
The Beilinson-Drinfeld Grassmannian and symplectic knot homology
Joel Kamnitzer
Seidel-Smith and Manolescu constructed knot homology theories using symplectic fibrations whose total spaces were certain varieties of matrices. These knot homology theories were a…
The crystal commutor and Drinfeld's unitarized R-matrix
Joel Kamnitzer, Peter Tingley
Drinfeld defined a unitarized R-matrix for any quantum group U_q(g). This gives a commutor for the category of U_q(g) representations, making it into a coboundary category. Henriqu…
A definition of the crystal commutor using Kashiwara's involution
Joel Kamnitzer, Peter Tingley
Henriques and Kamnitzer defined and studied a commutor for the category of crystals of a finite dimentional complex reductive Lie algebra. We show that the action of this commutor…
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…
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…