Infinite dimensional Lie algebras : an introduction / Victor G. Kac.
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| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boston :
Birkhäuser,
1983.
|
| Series: | Progress in mathematics (Boston, Mass.) ;
v. 44. |
| Subjects: |
Table of Contents:
- 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.