Zhu's algebra and the $C_2$-algebra in the symplectic and the orthogonal cases

Abstract

We prove that Zhu's algebra and the $C_2$-algebra of type ${\mathtt{C}}_m$ 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 to describe the whole $C_2$-algebras, we get only a description of a certain quotient of the algebra.

19 pages

References in corpus (2)

• Rationality, quasirationality and finite W-algebras
• Axiomatic Conformal Field Theory

Cited by in corpus (1)

• Spherical affine cones in exceptional cases and related branching rules