Affine braid group actions on derived categories of Springer resolutions

Categorical Affine Braid Group Action on Springer Resolutions

Braid Group Actions on Derived Categories of Coherent Sheaves

This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when dimX ≥ 2, our braid group actions are always faithful. We describe conjectural mirror s...

Braid group actions on categories of coherent sheaves

In this talk we will construct, following the recent paper [BR] by Bezrukavnikov and Riche, actions of certain groups on certain categories. Both the groups and the categories are relevant in representation theory, but all currently known constructions of the action are given by explicitly constructing action by generators and checking relations between them — this is what we will do. There are...

Geometric braid group action on derived categories of coherent sheaves

In this paper we give, for semi-simple groups without factors of type G2, a geometric construction of a braid group action on Db Coh(g̃) extending the action constructed by Bezrukavnikov, Mirković and Rumynin in the context of localization in positive characteristic. It follows that this action extends to characteristic zero, where it also has some nice representationtheoretic interpretations. T...

Artin group actions on derived categories of threefolds

Motivated by the enhanced gauge symmetry phenomenon of the physics literature and mirror symmetry, this paper constructs an action of an Artin group on the derived category of coherent sheaves of a smooth quasiprojective threefold containing a configuration of ruled surfaces described by a finite type Dynkin diagram. The action extends over deformations of the threefold via a compatible action ...