On the monoidality of Saito reflection functors

TL;DR

This paper extends the Saito reflection functor to symmetric Kac-Moody algebras and proves it has a monoidal structure, enhancing the understanding of these algebraic objects.

Contribution

It introduces a generalized Saito reflection functor for symmetric Kac-Moody algebras and establishes its monoidal property, which was previously unproven.

Findings

The Saito reflection functor is extended to symmetric Kac-Moody algebras.

The functor is proven to be monoidal.

This work broadens the applicability of reflection functors in algebraic representation theory.

Abstract

We extend the definition of the Saito reflection functor of the Khovanov- Lauda-Rouquier algebras to symmetric Kac-Moody algebra case and prove that it defines a monoidal functor.