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Catalogue Information
Field name	Details
Dewey Class	512.55
Title	Infinite Dimensional Lie Algebras ([EBook]) : An Introduction / by Victor G. Kac.
Author	Kac, Victor G. , 1943-
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser , 1983.
Physical Details	XVI, 252 p. : online resource.
Series	Progress in mathematics 0743-1643 ; ; 44
ISBN	9781475713824
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-1382-4
Links to Related Works	Subject References: Combinatorics . Differential Geometry . Lie groups . Mathematical Methods in Physics . Number Theory . Topological groups . Topology . Authors: Kac, Victor G. 1943- . Kac, Victor G., 1943- . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 512.55 .

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Infinite Dimensional Lie Algebras: An Introduction

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