درس‌هایی در نظریه نمایش و معادلات کنیژنیک-زامولودچیکوف

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. Content: 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. Deals with mathematical structures arising in conformal field theory and the $q$-deformations. This work presents a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. It is suitable for a one-semester graduate course.