卡茨-穆迪代数及其表示（英文版） 内容简介

本书系统地阐述Kac-Moody代数的结构与表示理论以及与组合论，数论，可积系统和物理的量子场论一些关系；特别地给出了Kac的专著``Infinite-dimensionalLiealgebras"中所缺的许多细节

卡茨-穆迪代数及其表示（英文版） 目录

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