2-Verma modules

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 modules.

Integrable Representations for the Extended Affine Lie Algebra Coordinated by Quantum Tori in Two Variables

In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by ℂq with finite-dimensional weight spaces and the center acting trivially, where ℂq is the quantum torus in two variables.