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2-Verma modules

Published 17 Oct 2017 in math.RT and math.QA | (1710.06293v3)

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.

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Authors (2)

  1. Grégoire Naisse 
  2. Pedro Vaz 

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