Infinite Dimensional Lie Algebras

Zur Zeit liegt uns keine Inhaltsangabe vor.

1. Basic definitions. - 2. The invariant bilinear form and the generalized Casimir operator. - 3. Integrable representations and the Weyl group of a Kac-Moody algebra. - 4. Some properties of generalized Cartan matrices. - 5. Real and imaginary roots. - 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group. - 7. Affine Lie algebras: the realization (case k = 1). - 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms. - 9. Highest weight modules over the Lie algebra g(A). - 10. Integrable highest weight modules: the character formula. - 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem. - 12. Integrable highest weight modules over affine Lie algebras. Application to ? -function identities. - 13. Affine Lie algebras, theta functions and modular forms. - 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations. - Index of notations and definitions. - References.