Braid group actions via categorified Heisenberg complexes

Abstract

AbstractWe construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel–Thomas) twists and are reminiscent of the Rickard complexes defined by Chuang–Rouquier. Conjecturally, one can relate our complexes to Rickard complexes using categorical vertex operators.