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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
eBookISBN:  978-1-4704-1285-2
Product Code:  SURV/58.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $50.40
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
eBook 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.

    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
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.

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
Please select which format for which you are requesting permissions.