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Braid group actions via categorified Heisenberg complexes

Published online by Cambridge University Press:  09 October 2013

Sabin Cautis*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2
Anthony Licata
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, Australia email [email protected]
Joshua Sussan
Affiliation:
Department of Mathematics, CUNY Medgar Evers, Brooklyn, NY, USA email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© The Author(s) 2013 

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