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＜電子ブック＞
Infinite Dimensional Lie Algebras : An Introduction / by Victor G. Kac
(Progress in Mathematics. ISSN:2296505X ; 44)

版	1st ed. 1983.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	1983
本文言語	英語
大きさ	XVI, 252 p : online resource
著者標目	*Kac, Victor G author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Mathematical physics LCSH:Topology LCSH:Geometry, Differential LCSH:Number theory LCSH:Discrete mathematics FREE:Topological Groups and Lie Groups FREE:Mathematical Methods in Physics FREE:Topology FREE:Differential Geometry FREE:Number Theory FREE:Discrete Mathematics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4757-1382-4

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