W-ALGEBRAS from HEISENBERG CATEGORIES

Sabin Cautis; Aaron D. Lauda; Anthony M. Licata; Joshua Sussan

doi:10.1017/S1474748016000189

W-ALGEBRAS from HEISENBERG CATEGORIES

Sabin Cautis, Aaron D. Lauda, Anthony M. Licata, Joshua Sussan

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

12 Citations (Scopus)

Abstract

The trace (or zeroth Hochschild homology) of Khovanov's Heisenberg category is identified with a quotient of the algebra W₁+∞. This induces an action of W₁+∞ on the center of the categorified Fock space representation, which can be identified with the action of W₁+∞ on symmetric functions.

Original language	English
Pages (from-to)	981-1017
Number of pages	37
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	17
Issue number	5
DOIs	https://doi.org/10.1017/S1474748016000189
Publication status	Published - 1 Nov 2018

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title = "W-ALGEBRAS from HEISENBERG CATEGORIES",

abstract = "The trace (or zeroth Hochschild homology) of Khovanov's Heisenberg category is identified with a quotient of the algebra W1+∞. This induces an action of W1+∞ on the center of the categorified Fock space representation, which can be identified with the action of W1+∞ on symmetric functions.",

keywords = "Heisenberg algebra, Heisenberg category, Hochschild homology, W-algebras, categorification, trace",

author = "Sabin Cautis and Lauda, {Aaron D.} and Licata, {Anthony M.} and Joshua Sussan",

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AU - Lauda, Aaron D.

AU - Licata, Anthony M.

AU - Sussan, Joshua

N1 - Publisher Copyright: © Cambridge University Press 2016.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - The trace (or zeroth Hochschild homology) of Khovanov's Heisenberg category is identified with a quotient of the algebra W1+∞. This induces an action of W1+∞ on the center of the categorified Fock space representation, which can be identified with the action of W1+∞ on symmetric functions.

AB - The trace (or zeroth Hochschild homology) of Khovanov's Heisenberg category is identified with a quotient of the algebra W1+∞. This induces an action of W1+∞ on the center of the categorified Fock space representation, which can be identified with the action of W1+∞ on symmetric functions.

KW - Heisenberg algebra

KW - Heisenberg category

KW - Hochschild homology

KW - W-algebras

KW - categorification

KW - trace

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U2 - 10.1017/S1474748016000189

DO - 10.1017/S1474748016000189

M3 - Article

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EP - 1017

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 5

ER -

W-ALGEBRAS from HEISENBERG CATEGORIES

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