Representations of the vertex algebra W1+∞ with a negative integer central charge

Let D be the Lie algebra of regular differential operators on C\{0}, and (D) over cap = D + CC be the central extension of D. Let W-1+infinity,W--N be the vertex algebra associated to the irreducible vacuum D-module with the central charge c = -N. We show that W-1+infinity,W--N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W1+infinity -N-modules. Considering these modules as (D) over cap -modules, we identify the corresponding highest weights.