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

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

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