This book is devoted to mathematical structures arising in conformal field theory and the \(q\)-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

• Introduction
• Representations of finite-dimensional and affine Lie algebras
• Knizhnik-Zamolodchikov equations
• Solutions of the Knizhnik-Zamolodchikov equations
• Free field realization
• Quantum groups
• Local systems and configuration spaces
• Monodromy of the Knizhnik-Zamolodchikov equations
• Quantum affine algebras
• Quantum Knizhnik-Zamolodchikov equations
• Solutions of the quantum Knizhnik-Zamolodchikov equations for \(\mathfrak {sl}_2\)
• Connection matrices for the quantum Knizhnik-Zamolodchikov equations and elliptic functions
• Current developments and future perspectives
• References
• Index