Infinite Dimensional Lie Algebras - Victor G. Kac

Infinite Dimensional Lie Algebras

An Introduction

(Autor)

Buch | Softcover
252 Seiten
2012
Birkhauser Boston Inc (Verlag)
978-1-4757-1384-8 (ISBN)
106,99 inkl. MwSt

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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