A definition of the crystal commutor using Kashiwara's involution
arXiv:math/0610952
Abstract
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 on highest weight elements can be expressed very simply using Kashiwara's involution on the Verma crystal.
5 pages