ausblenden:
Schlagwörter:
Mathematics, Representation Theory, Quantum Algebra
Zusammenfassung:
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.