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

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