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W-ALGEBRAS FROM HEISENBERG CATEGORIES

Part of: Categories with structure Groups and algebras in quantum theory Representation theory of groups Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  13 July 2016

Sabin Cautis ,
Aaron D. Lauda ,
Anthony M. Licata  and
Joshua Sussan
Sabin Cautis
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada (cautis@math.ubc.ca)
Aaron D. Lauda
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA, USA (lauda@usc.edu)
Anthony M. Licata
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, Australia (anthony.licata@anu.edu.au)
Joshua Sussan
Affiliation:
Department of Mathematics, CUNY Medgar Evers, Brooklyn, NY, USA (jsussan@mec.cuny.edu)
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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.

Keywords

Heisenberg algebracategorificationW-algebrasHochschild homologytraceHeisenberg category

MSC classification

Primary: 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations 20C08: Hecke algebras and their representations 17B65: Infinite-dimensional Lie (super)algebras 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 5 , November 2018 , pp. 981 - 1017
Copyright
© Cambridge University Press 2016 

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