Infinite dimensional Lie algebras
著者
書誌事項
Infinite dimensional Lie algebras
Cambridge University Press, 1985
2nd ed
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注記
Bibliography: p. 261-277
Includes index
内容説明・目次
内容説明
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody 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.
目次
- 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.
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