Аннотация:
I will speak about my joint work with Yury Volkov where we prove that the
action of a generalised braid group on an enhanced triangulated category via
spherical twists along an ADE-configuration of n-spherical objects is faithful for any
integer n not equal to 1. Although various results on the faithfulness of this action
have been obtain over the years (e.g. for type A or n=2, and in some other cases),
the approach we present allows us to establish the faithfulness for any ADE diagram, any enhanced triangulated category, and any n not equal to 1 almost simultaneously.
