Biadjointness in Cyclotomic Khovanov–Lauda–Rouquier Algebras

Abstract

In this paper, we prove that a pair of functors ${\mathsf{E}}_1^{\Lambda }$ and ${\mathsf{F}}_1^{\Lambda }$ appearing in the categorification of irreducible highest weight modules of quantum groups via cyclotomic Khovanov-Lauda-Rouquier algebras is a biadjoint pair.