Zhu's algebra and the C₂-algebra in the symplectic and the orthogonal cases

We prove that Zhu's algebra and the C₂-algebra of type have the same dimension, and we compute the graded character of the latter. Maximal parabolic subalgebras of the symplectic algebra play a central role in our construction. For the orthogonal algebras our methods do not allow us to describe the whole C₂-algebras; we get only a description of a certain quotient of the algebra.