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Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

Pavel I. Etingof Harvard University, Cambridge, MA
Igor B. Frenkel Yale University, New Haven, CT
Alexander A. Kirillov, Jr. Massachusetts Institute of Technology, Cambridge, MA
Available Formats:
Electronic ISBN: 978-1-4704-1285-2
Product Code: SURV/58.E
List Price: $63.00 MAA Member Price:$56.70
AMS Member Price: $50.40 Click above image for expanded view Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations Pavel I. Etingof Harvard University, Cambridge, MA Igor B. Frenkel Yale University, New Haven, CT Alexander A. Kirillov, Jr. Massachusetts Institute of Technology, Cambridge, MA Available Formats:  Electronic ISBN: 978-1-4704-1285-2 Product Code: SURV/58.E  List Price:$63.00 MAA Member Price: $56.70 AMS Member Price:$50.40
• Book Details

Mathematical Surveys and Monographs
Volume: 581998; 198 pp
MSC: Primary 81; Secondary 17;

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.

Graduate students and research mathematicians interested in mathematical physics.

• Chapters
• Lecture 1. Introduction
• Lecture 2. Representations of finite-dimensional and affine Lie algebras
• Lecture 3. Knizhnik-Zamolodchikov equations
• Lecture 4. Solutions of the Knizhnik-Zamolodchikov equations
• Lecture 5. Free field realization
• Lecture 6. Quantum groups
• Lecture 7. Local systems and configuration spaces
• Lecture 8. Monodromy of Knizhnik-Zamolodchikov equations
• Lecture 9. Quantum affine algebras
• Lecture 10. Quantum Knizhnik-Zamolodchikov equations
• Lecture 11. Solutions of the quantum Knizhnik-Zamolodchikov equations for $\mathfrak {sl}_2$
• Lecture 12. Connection matrices for the quantum Knizhnik-Zamolod- chikov equations and elliptic functions
• Lecture 13. Current developments and future perspectives

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 581998; 198 pp
MSC: Primary 81; Secondary 17;

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.

Graduate students and research mathematicians interested in mathematical physics.

• Chapters
• Lecture 1. Introduction
• Lecture 2. Representations of finite-dimensional and affine Lie algebras
• Lecture 3. Knizhnik-Zamolodchikov equations
• Lecture 4. Solutions of the Knizhnik-Zamolodchikov equations
• Lecture 5. Free field realization
• Lecture 6. Quantum groups
• Lecture 7. Local systems and configuration spaces
• Lecture 8. Monodromy of Knizhnik-Zamolodchikov equations
• Lecture 9. Quantum affine algebras
• Lecture 10. Quantum Knizhnik-Zamolodchikov equations
• Lecture 11. Solutions of the quantum Knizhnik-Zamolodchikov equations for $\mathfrak {sl}_2$
• Lecture 12. Connection matrices for the quantum Knizhnik-Zamolod- chikov equations and elliptic functions
• Lecture 13. Current developments and future perspectives
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
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