by Minoru Wakimoto (Kyushu University, Japan)

The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.

• Preliminaries on Affine Lie Algebras
• Characters of Integrable Representations
• Principal Admissible Weights
• Residue of Principal Admissible Characters
• Characters of Affine Orbifolds
• Operator Calculus
• Branching Functions
• W-Algebra
• Vertex Representations for Affine Lie Algebras
• Soliton Equations