Braid group actions via categorified Heisenberg complexes

TL;DR

This paper constructs categorical braid group actions using 2-representations of a Heisenberg algebra, generalizing known twists and proposing a connection to Rickard complexes via categorical vertex operators.

Contribution

It introduces a new method to realize braid group actions categorically through complexes derived from Heisenberg algebra representations.

Findings

Constructed categorical braid group actions from 2-representations.

Generalized spherical twists to new complexes.

Proposed a conjectural link to Rickard complexes via vertex operators.

Abstract

We 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.