REPRESENTATIONS OF THE VERTEX ALGEBRA W_1+∞ WITH A NEGATIVE INTEGER CENTRAL CHARGE

Abstract

Let D be the Lie algebra of regular differential operators on , and be the central extension of D. Let W _{1+∞,minus;N} be the vertex algebra associated to the irreducible vacuum -module with the central charge c = −N. We show that W _1+∞,−N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W _1+∞,−N -modules. Considering these modules as -modules, we identify the corresponding highest weights.

Acknowledgments