Infinite Dimensional Lie Algebras
Birkhauser Boston Inc (Verlag)
978-1-4757-1384-8 (ISBN)
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.
| Reihe/Serie | Progress in Mathematics ; 44 |
|---|---|
| Zusatzinfo | XVI, 252 p. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4757-1384-3 / 1475713843 |
| ISBN-13 | 978-1-4757-1384-8 / 9781475713848 |
| Zustand | Neuware |
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