Some Rational Vertex Algebras

Let $L((n-\tfrac 3 2)\Lambda_0)$, $n \in \Bbb N$, be a vertex operator algebra associated to the irreducible highest weight module $L((n-\tfrac 3 2)\Lambda_0)$ for a symplectic affine Lie algebra. We find a complete set of irreducible modules for $L((n-\tfrac 3 2)\Lambda_0)$ and show that every module for $L((n-\tfrac 3 2)\Lambda_0)$ from the category $\Cal O$ is completely reducible.