Representations of the vertex algebra $W_{1+\infty }$ with a negative integer central charge

Abstract

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

14 pages, Latex

References in corpus (3)

• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• W_{1+\infty} and W(gl_N) with central charge N
• W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization

Cited by in corpus (1)

• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion