Crystals from categorified quantum groups
arXiv:0909.1810 · doi:10.1016/j.aim.2011.06.009
Abstract
We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group.
56 pages, 6 eps files. v2 corrects typos