W-ALGEBRAS FROM HEISENBERG CATEGORIES. (13th July 2016)

• Record Type: Journal Article
• Authors: Cautis, Sabin; Lauda, Aaron D.; Licata, Anthony M.; Sussan, Joshua
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 17:Number 5(2018)
• Page Start: 981
• Page End: 1017
• Publication Date: 2016-07-13
• Subjects: 81R10, -- 20C08, -- 17B65, -- 18D10; Heisenberg algebra, -- categorification, -- W-algebras, -- Hochschild homology, -- trace, -- Heisenberg category; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748016000189
• Languages: English
• ISSNs: 1474-7480

Abstract

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.