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W-ALGEBRAS FROM HEISENBERG CATEGORIES

Published online by Cambridge University Press:  13 July 2016

Sabin Cautis
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada ([email protected])
Aaron D. Lauda
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA, USA ([email protected])
Anthony M. Licata
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, Australia ([email protected])
Joshua Sussan
Affiliation:
Department of Mathematics, CUNY Medgar Evers, Brooklyn, NY, USA ([email protected])

Abstract

The trace (or zeroth Hochschild homology) of Khovanov’s Heisenberg category is identified with a quotient of the algebra $W_{1+\infty }$. This induces an action of $W_{1+\infty }$ on the center of the categorified Fock space representation, which can be identified with the action of $W_{1+\infty }$ on symmetric functions.

Type
Research Article
Copyright
© Cambridge University Press 2016 

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