Mathematical Surveys and Monographs 1998; 198 pp; hardcover Volume: 58 ISBN10: 0821804960 ISBN13: 9780821804964 List Price: US$60 Member Price: US$48 Order Code: SURV/58
 This book is devoted to mathematical structures arising in conformal field theory and the \(q\)deformations. The authors give a selfcontained exposition of the theory of KnizhnikZamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a onesemester graduate course. Readership Graduate students and research mathematicians interested in mathematical physics. Table of Contents  Introduction
 Representations of finitedimensional and affine Lie algebras
 KnizhnikZamolodchikov equations
 Solutions of the KnizhnikZamolodchikov equations
 Free field realization
 Quantum groups
 Local systems and configuration spaces
 Monodromy of the KnizhnikZamolodchikov equations
 Quantum affine algebras
 Quantum KnizhnikZamolodchikov equations
 Solutions of the quantum KnizhnikZamolodchikov equations for \(\mathfrak {sl}_2\)
 Connection matrices for the quantum KnizhnikZamolodchikov equations and elliptic functions
 Current developments and future perspectives
 References
 Index
