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

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

1999-04-13

arxiv.org/abs/math/9904057v1

Communications in Algebra 29(7) (2001) 3153-3166

Mathematics

Quantum Algebra

14 pages, Latex

Scientific paper

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 $2 N$ 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.

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