Classification of Harish-Chandra Modules

We explain the proof of the conjecture of V. Kac which says that any simple ℤ-graded Vir-module with finite multiplicities is either a highest weight module, a lowest weight module, or the module of type t λ ℂ[t,t −1](dt) μ . The proof is given by the reduction to positive characteristic cases. Hence, for the reader who is not familiar with Lie p-algebras and their representations, we make a brief survey of the general theory of Lie p-algebras in Appendix B that are used in the proof. This chapter can be read independently of other chapters.