|
" Infinite Dimensional Lie Algebras "
by Victor G. Kac.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
574547
|
| Doc. No
|
:
|
b403766
|
| Main Entry
|
:
|
Kac, Victor G.
|
| Title & Author
|
:
|
Infinite Dimensional Lie Algebras : An Introduction /\ by Victor G. Kac.
|
| Publication Statement
|
:
|
Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 1983.
|
| Series Statement
|
:
|
Progress in Mathematics ;; 44
|
| ISBN
|
:
|
9781475713824
|
|
|
:
|
: 9781475713848
|
| 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.
|
| Subject
|
:
|
Mathematics.
|
| Subject
|
:
|
Topological Groups.
|
| Subject
|
:
|
Combinatorics.
|
| Subject
|
:
|
Global differential geometry.
|
| Subject
|
:
|
Number theory.
|
| Subject
|
:
|
Topology.
|
| Subject
|
:
|
Mathematical physics.
|
| Added Entry
|
:
|
SpringerLink (Online service)
|
| |