“Infinite”

. Let S be a smooth projective surface. Using correspondences, we construct an infinite dimensional Lie algebra that acts on the direct sum of the cohomology groups of the incidence Hilbert schemes S [ m,m +1] . The algebra is related to an extension of an infinite dimensional Heisenberg algebra. The space e H S is a highest weight representation of this algebra. Our result provides a representation-theoretic interpretation of Cheah’s generating function of Betti numbers of the incidence Hilbert schemes. As a consequence, an additive basis of H ∗ ( S [ m,m +1] ) is obtained.