Infinite-Dimensional Lie Algebras

by Victor G. Kac

• ISBN13: 9780521466936
• ISBN10: 0521466938
• Edition: 3rd
• Format: Paperback
• Copyright: 1994-08-26
• Publisher: Cambridge University Press

Summary

This is the third, substantially revised edition of this important monograph. The book is concerned with KacMoody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.

Table of Contents

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 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

Application to n-function identities

Sugawara operators and branching functions

13. Affine algebras, theta functions, and modular forms

14. The principal and homogeneous vertex operator constructions of the basic representation

Boson-Fermion correspondence

Application to soliton equations.