  A W-algebra action is constructed on the equivariant Borel-Moore homology of
the Hilbert scheme of points on a nonreduced plane in three dimensional affine
space, identifying it to the vacuum W-module. This is based on a generalization
of the ADHM construction as well as the W-action on the equivariant Borel-Moore
homology of the moduli space of instantons constructed by Schiffmann and
Vasserot.
