THE ANNIHILATING IDEALS OF MINIMAL MODELS

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of W(n) algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structures of quasi-finite modules of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of W(n) and W(l) algebras at the same central charge are isomorphic to each other.