2-Verma modules

Naisse, Grégoire; Vaz, Pedro

doi:10.1515/crelle-2021-0046

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2-Verma modules

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Naisse, Grégoire
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1515/crelle-2021-0046
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Citation

Naisse, G., & Vaz, P. (2022). 2-Verma modules. Journal für die reine und angewandte Mathematik, 2022(782), 43-108. doi:10.1515/crelle-2021-0046.

Cite as: https://hdl.handle.net/21.11116/0000-0009-EFA6-F

Abstract

We construct a categorification of parabolic Verma modules for symmetrizable
Kac-Moody algebras using KLR-like diagrammatic algebras. We show that our
construction arises naturally from a dg-enhancement of the cyclotomic quotients
of the KLR-algebras. As a consequence, we are able to recover the usual
categorification of integrable modules. We also introduce a notion of
dg-2-representation for quantum Kac--Moody algebras, and in particular of
parabolic 2-Verma module.