Categorification of the internal braid group action for quantum groups I: 2-functoriality

TL;DR

This paper constructs 2-functors on the categorified quantum group of simply-laced Kac-Moody algebras, which realize Lusztig's internal braid group action at the Grothendieck group level, advancing categorification theory.

Contribution

It introduces a new 2-functorial framework that lifts Lusztig's braid group action to the categorified quantum group setting.

Findings

Defined 2-functors inducing braid group actions

Established functoriality at the categorified level

Connected categorification with Lusztig's algebraic structures

Abstract

We define 2-functors on the categorified quantum group of a simply-laced Kac-Moody algebra that induce Lusztig's internal braid group action at the level of the Grothendieck group.