Victor G. Kac

Infinite dimensional lie algebras - New York: Springer, [c1983] - 245 p - Progress in Mathematics Vol. 44 .

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

9781475713848


Mathematics

QA252.3