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.