Rationality, Quasirationality and Finite W-Algebras.

: Some of the consequences that follow from the C2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C2 condition has only finitely many n-point functions, and this result is used to prove a version of a conjecture of Nahm, namely that every representation of such a conformal field theory is quasirational. We also show that every such vertex operator algebra is a finite W-algebra, and we give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules. [ABSTRACT FROM AUTHOR]