Implicit structure in 2-representations of quantum groups
arXiv:1111.1431 · doi:10.1007/s00029-014-0162-x
Abstract
Given a strong 2-representation of a Kac-Moody Lie algebra (in the sense of Rouquier) we show how to extend it to a 2-representation of categorified quantum groups (in the sense of Khovanov-Lauda). This involves checking certain extra 2-relations which are explicit in the definition by Khovanov-Lauda and, as it turns out, implicit in Rouquier's definition. Some applications are also discussed.
33 pages, xypic diagrams; v2 corrects typos in section 7; v3 final version