Infinite Dimensional Lie Algebras : An Introduction

Chapter 1 Basic definitions

Chapter 2 The invariant bilinear form and the generalized Casimir operator

Chapter 3 Integrable representations and the Weyl group of a Kac-Moody algebra

Chapter 4 Some properties of generalized Cartan matrices

Chapter 5 Real and imaginary roots

Chapter 6 Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group

Chapter 8 Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms

Chapter 9 Highest weight modules over the Lie algebra g( A )

Chapter 10 Integrable highest weight modules: the character formula

Chapter 11 Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem

Chapter 12 Integrable highest weight modules over affine Lie algebras. Application to η -function identities

Chapter 13 Affine Lie algebras, theta functions and modular forms

Chapter 14 The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations