Implicit structure in 2-representations of quantum groups
Quantum Algebra
2015-02-24 v3 Representation Theory
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.
Cite
@article{arxiv.1111.1431,
title = {Implicit structure in 2-representations of quantum groups},
author = {Sabin Cautis and Aaron D. Lauda},
journal= {arXiv preprint arXiv:1111.1431},
year = {2015}
}
Comments
33 pages, xypic diagrams; v2 corrects typos in section 7; v3 final version