W-algebras from Heisenberg categories

TL;DR

This paper establishes a connection between the trace of Khovanov's Heisenberg category and the algebra W_{1+ finite}, leading to an action of W_{1+ finite} on symmetric functions, thus linking categorification with algebraic structures.

Contribution

It identifies the trace of the Heisenberg category with a quotient of W_{1+ finite} and constructs an action on symmetric functions, bridging categorification and algebra.

Findings

Trace of Heisenberg category is a quotient of W_{1+ finite}

W_{1+ finite} acts on symmetric functions

Provides new insights into categorification and algebraic actions

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 symmetric functions.