Crystals from categorified quantum groups
Representation Theory
2011-08-02 v2
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.
Keywords
Cite
@article{arxiv.0909.1810,
title = {Crystals from categorified quantum groups},
author = {Aaron D. Lauda and Monica Vazirani},
journal= {arXiv preprint arXiv:0909.1810},
year = {2011}
}
Comments
56 pages, 6 eps files. v2 corrects typos