5 citations · 5 across the 1 of their papers we have counts for
4 papers
Crystal bases and two-sided cells of quantum affine algebras
Jonathan Beck, Hiraku Nakajima
Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We construct a basis of $\U^+$ whi…
Crystal structure of level zero extremal weight modules
Jonathan Beck
We consider the crystal structure of the level zero extremal weight modules using the crystal base of the quantum affine algebra constructed by Beck, Chari and Pressley. Thi…
An Algebraic Characterization of the Affine Canonical Basis
Jonathan Beck, Vyjayanthi Chari, Andrew Pressley
The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the…
Canonical Basis and Macdonald Polynomials
Jonathan Beck, Igor Frenkel, Naihuan Jing
In the basic representation of realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2…