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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
Front Cover for Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
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
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Front Cover for Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
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  • Front Cover for Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
  • Back Cover for Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
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
Add to cart
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 58; 1998; 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.
    Readership

    Graduate students and research mathematicians interested in mathematical physics.
  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • 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
Mathematical Surveys and Monographs
Volume: 58; 1998; 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.
Readership

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
Accessibility – to request an alternate format of an AMS title
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