Faithful actions of braid groups by twists along ADE-configurations of spherical objects

TL;DR

This paper proves that generalized braid groups act faithfully on certain triangulated categories via spherical twist functors, extending understanding of braid group actions in algebraic geometry and representation theory.

Contribution

It establishes the faithfulness of braid group actions generated by spherical twists along ADE-configurations for all integers except one.

Findings

Braid group actions are faithful for ADE-configurations.

Faithfulness holds for all integer parameters except one.

Advances the understanding of braid group representations in derived categories.

Abstract

We prove that the action of a generalized braid group on an enhanced triangulated categories, generated by spherical twist functors along an ADE-configuration of $\omega$-spherical objects, is faithful for any integer $\omega \neq 1$.