Some Rational Vertex Algebras

Abstract

Let $L((n-\frac{3}{2}){\Lambda }_0)$, $n\in \mathbb{N}$, be a vertex operator algebra associated to the irreducible highest weight module $L((n-\frac{3}{2}){\Lambda }_0)$ for a symplectic affine Lie algebra. We find a complete set of irreducible modules for $L((n-\frac{3}{2}){\Lambda }_0)$ and show that every module for $L((n-\frac{3}{2}){\Lambda }_0)$ from the category $\Cal O$ is completely reducible.

14 pages, AMSTEX

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