Braid group actions via categorified Heisenberg complexes

Sabin Cautis; Anthony Licata; Joshua Sussan

doi:10.1112/S0010437X13007367

Braid group actions via categorified Heisenberg complexes

Sabin Cautis, Anthony Licata, Joshua Sussan

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	105-142
Number of pages	38
Journal	Compositio Mathematica
Volume	150
Issue number	1
DOIs	https://doi.org/10.1112/S0010437X13007367
Publication status	Published - Jan 2014

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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.",

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AB - 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.

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Braid group actions via categorified Heisenberg complexes

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