On a braid group action

TL;DR

This paper explores the implications of invertible Rickard complexes within categorified quantum groups, leading to new insights into reflection functors and the restriction of categorical representations.

Contribution

It introduces a novel analysis of invertible Rickard complexes, connecting them to reflection functors and face restrictions in categorical representations.

Findings

Description of reflection functors for quiver Hecke algebras

Development of a theory for restricting categorical representations along a face

Insights into the structure of categorified quantum groups

Abstract

We discuss some consequences of the invertibility of Rickard complexes in a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations along a face.