Categorification of highest weight modules over quantum generalized Kac-Moody algebras

TL;DR

This paper proves that cyclotomic Khovanov-Lauda-Rouquier algebras categorify integrable highest weight modules over quantum generalized Kac-Moody algebras, establishing a deep link between algebraic structures and categorification.

Contribution

It demonstrates that cyclotomic Khovanov-Lauda-Rouquier algebras provide a categorification of highest weight modules over quantum generalized Kac-Moody algebras, a novel connection in representation theory.

Findings

Cyclotomic Khovanov-Lauda-Rouquier algebras categorify highest weight modules.

Establishment of a correspondence between algebraic modules and categorified structures.

Advancement in understanding the categorification of quantum generalized Kac-Moody algebras.

Abstract

Let $U_q(\g)$ be a quantum generalized Kac-Moody algebra and let $V(\Lambda)$ be the integrable highest weight $U_q(\g)$-module with highest weight $\Lambda$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^\Lambda$ provides a categorification of $V(\Lambda)$.