Implicit structure in 2-representations of quantum groups

Details Implicit structure in 2-representations of quantum groups Implicit structure in 2-representations of quantum groups

2011-11-06

arxiv.org/abs/1111.1431v2

Mathematics

Quantum Algebra

33 pages, xypic diagrams; v2 corrects typos in section 7

Scientific paper

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.

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