Biadjointness in cyclic Khovanov-Lauda-Rouquier Algebras

TL;DR

This paper proves that the simple root functors E and F in the categorification of quantum group modules via cyclotomic Khovanov-Lauda-Rouquier algebras form a biadjoint pair, clarifying their categorical structure.

Contribution

It establishes the biadjointness of root functors in the categorification framework, a key property previously unproven in this context.

Findings

E and F are biadjoint functors in this categorification

Provides a rigorous proof of biadjointness for simple root functors

Enhances understanding of the categorical structure of quantum group representations

Abstract

We prove that the simple root functors E and F appearing in the categorification of irreducible highest weight modules of quantum groups via cyclotomic Khovanov-Lauda-Rouquier algebras is a biadjoint pair.