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Klappentext The third! substantially revised edition of a monograph concerned with Kac-Moody algebras! a particular class of infinite-dimensional Lie albegras! and their representations! based on courses given over a number of years at MIT and in Paris. Suitable for graduate courses. Zusammenfassung This is the third! substantially revised edition of this important monograph and graduate text. Each chapter begins with a motivating discussion and ends with a collection of exercises! with hints to the more challenging problems. The theory has applications in many areas of mathematics and mathematical physics and these are discussed in relation to the basic theory where appropriate. Inhaltsverzeichnis Introduction; Notational conventions; 1. Basic definitions; 2. The invariant bilinear form and the generalized casimir operator; 3. Integrable representations of Kac-Moody algebras and the weyl group; 4. A classification of generalized cartan matrices; 5. Real and imaginary roots; 6. Affine algebras: the normalized cartan invariant form, the root system, and the weyl group; 7. Affine algebras as central extensions of loop algebras; 8. Twisted affine algebras and finite order automorphisms; 9. Highest-weight modules over Kac-Moody algebras; 10. Integrable highest-weight modules: the character formula; 11. Integrable highest-weight modules: the weight system and the unitarizability; 12. Integrable highest-weight modules over affine algebras; 13. Affine algebras, theta functions, and modular forms; 14. The principal and homogeneous vertex operator constructions of the basic representation; Index of notations and definitions; References; Conference proceedings and collections of paper.
