Braid group actions via categorified Heisenberg complexes

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.

35 pages

References in corpus (4)

• 2-Kac-Moody algebras
• Derived equivalences for symmetric groups and sl\_2-categorification
• Categorification of the braid groups
• Vertex operators and 2-representations of quantum affine algebras

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