Implicit structure in 2-representations of quantum groups

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

References in corpus (1)

• A diagrammatic approach to categorification of quantum groups III

Cited by in corpus (14)

• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• On the center of quiver-Hecke algebras
• An approach to categorification of some small quantum groups II
• Categorified skew Howe duality and comparison of knot homologies
• A categorical action on quantized quiver varieties
• An approach to categorification of Verma modules
• Remarks on coloured triply graded link invariants
• Super Kac-Moody 2-categories
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• A categorification of a quantum Frobenius map
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Parameters in categorified quantum groups
• Curved Rickard complexes and link homologies
• Categorification of the internal braid group action for quantum groups I: 2-functoriality