Electronic ISBN:  9781470412852 
Product Code:  SURV/58.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $50.40 

Book DetailsMathematical Surveys and MonographsVolume: 58; 1998; 198 ppMSC: Primary 81; Secondary 17;
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.
ReadershipGraduate students and research mathematicians interested in mathematical physics.

Table of Contents

Chapters

Lecture 1. Introduction

Lecture 2. Representations of finitedimensional and affine Lie algebras

Lecture 3. KnizhnikZamolodchikov equations

Lecture 4. Solutions of the KnizhnikZamolodchikov equations

Lecture 5. Free field realization

Lecture 6. Quantum groups

Lecture 7. Local systems and configuration spaces

Lecture 8. Monodromy of KnizhnikZamolodchikov equations

Lecture 9. Quantum affine algebras

Lecture 10. Quantum KnizhnikZamolodchikov equations

Lecture 11. Solutions of the quantum KnizhnikZamolodchikov equations for $\mathfrak {sl}_2$

Lecture 12. Connection matrices for the quantum KnizhnikZamolod chikov equations and elliptic functions

Lecture 13. Current developments and future perspectives


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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.
Graduate students and research mathematicians interested in mathematical physics.

Chapters

Lecture 1. Introduction

Lecture 2. Representations of finitedimensional and affine Lie algebras

Lecture 3. KnizhnikZamolodchikov equations

Lecture 4. Solutions of the KnizhnikZamolodchikov equations

Lecture 5. Free field realization

Lecture 6. Quantum groups

Lecture 7. Local systems and configuration spaces

Lecture 8. Monodromy of KnizhnikZamolodchikov equations

Lecture 9. Quantum affine algebras

Lecture 10. Quantum KnizhnikZamolodchikov equations

Lecture 11. Solutions of the quantum KnizhnikZamolodchikov equations for $\mathfrak {sl}_2$

Lecture 12. Connection matrices for the quantum KnizhnikZamolod chikov equations and elliptic functions

Lecture 13. Current developments and future perspectives