2-Verma modules
Representation Theory
2021-07-23 v3 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1710.06293,
title = {2-Verma modules},
author = {Grégoire Naisse and Pedro Vaz},
journal= {arXiv preprint arXiv:1710.06293},
year = {2021}
}
Comments
v3, reviewed version with minor fixes, 67pp