| Xiaoping Xu，a professor at Institute of Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences． |
| Preface Notational Conventions Introduction Chapter 1 Structure of Kac-Moody Algebras 1.1 Lie Algebra Associated with a Matrix 1.2 Invariant Bilinear Form 1.3 Generalized Casimir Operators 1.4 Weyl Groups 1.5 Classification of Generalized Cartan Matrices 1.6 Real and Imaginary Roots Chapter 2 Affine Kac-Moody Algebras 2.1 Affine Roots and Weyl Groups 2.2 Realizations of Untwisted Affine Algebras 2.3 Realizations of Twisted Affine Algebras Chapter 3 Representation Theory 3.1 Highest-Weight Modules 3.2 Defining Relations of Kac-Moody Algebras 3.3 Character Formula 3.4 Weights 3.5 Unit arizability 3.6 Action of Imaginary Root Vectors 3.7 Implications of the Denominator Identity Chapter 4 Representations of Afllne and Virasoro Algebras. 4.1 Macdonald Identities 4.2 Affine Weights 4.3 Virasoro Algebra 4.4 Sugawara Construction 4.5 Coset Construction Chapter 5 Related Modular Forms 5.1 Theta Functions 5.2 Modular Transformations 5.3 Modular Forms 5.4 Applications to Affine Algebras Chapter 6 Realizations of Modules 6.1 Generating Functions 6.2 Untwisted Vertex Operator Representations 6.3 Twisted Vertex Operator Representations 6.4 Free Fermionic Field Realizations 6.5 Boson-Fermion C0rreSpondenCe Bibliography Index |
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