  Let C be a proper, integral, locally planar curve, and consider its Hilbert
schemes of points C^[n]. We define 4 creation/annihilation operators acting on
the rational homology groups of these Hilbert schemes and show that the
operators satisfy the relations of a Weyl algebra. The action of this algebra
is similar to that defined by Grojnowski and Nakajima for a smooth surface.
  As a corollary, we compute the cohomology of C^[n] in terms of the cohomology
of the compactified Jacobian of C together with an auxiliary grading on the
latter. This recovers and slightly strenghtens a formula recently obtained in a
different way by Maulik and Yun and independently Migliorini and Shende.
