English

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

R2 v1 2026-06-22T22:16:56.388Z