Infinite Dimensional Lie Algebras: An Introduction

Front Matter....Pages i-xvi
Basic definitions....Pages 1-13
The invariant bilinear form and the generalized Casimir operator....Pages 14-24
Integrable representations and the Weyl group of a Kac-Moody algebra....Pages 25-37
Some properties of generalized Cartan matrices....Pages 38-49
Real and imaginary roots....Pages 50-62
Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group....Pages 63-72
Affine Lie algebras: the realization (case k=1)....Pages 73-88
Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms....Pages 89-102
Highest weight modules over the Lie algebra g( A )....Pages 103-118
Integrable highest weight modules: the character formula....Pages 119-133
Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem....Pages 134-149
Integrable highest weight modules over affine Lie algebras. Application to η -function identities....Pages 150-164
Affine Lie algebras, theta functions and modular forms....Pages 165-189
The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations....Pages 190-225
Back Matter....Pages 226-252