Given a finite subgroup we define an additive -category whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions .
"Heisenberg categorification and Hilbert schemes." Duke Math. J. 161 (13) 2469 - 2547, 1 October 2012. https://doi.org/10.1215/00127094-1812726