Expanded lecture notes of a summer school at the University of Algarve, Portugal
Written by leading experts in the field
Extensive review of factorization theory, its application to integrable systems, and its developments over the last 25 years
This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.
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In September 2000 a Summer School on "Factorization and Integrable Systems" was held at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field. The lecture notes of the courses have been specially prepared for publication in this volume.
The book consists of four contributions. I. Gohberg, M.A. Kaashoek and I.M. Spitkovsky present an extensive review of the factorization theory of matrix functions relative to a curve, with emphasis on the developments of the last 20-25 years. The group-theoretical approach to classical integrable systems is reviewed by M.A. Semenov-Tian-Shansky. P.P. Kulish surveyed the quantum inverse scattering method using the isotropic Heisenberg spin chain as the main example.
An Overview of Matrix Factorization Theory and Operator Applications.- 0 Introduction.- 1 General theorems.- 2 Factorization in decomposing Banach algebras.- 3 Generalized Lp factorization.- 4 State space method.- References.- Matrix Riemann-Hilbert Problems Related to Branched Coverings of ??1.- 1 Introduction.- 2 Riemann-Hilbert problem with quasi-permutation monodromies and algebraic curves.- 3 Riemann surfaces. Rauch variational formulas.- 4 Solution of Riemann-Hilbert problems with quasi-permutation monodromies and Szegö kernel.- 5 Isomonodromic tau-function and Cauchy-Riemann determinants.- Acknowledgements.- References.- Quantum Groups and Integrable Models.- 1 Introduction.- 2 Algebraic Bethe Ansatz and QISM.- 3 Yang-Baxter equation.- 4 Thermodynamic limits.- 5 Conclusion.- Acknowledgements.- References.- Integrable Systems and Factorization Problems.- 1 Introduction.- 2 A few preliminaries: Poisson brackets, coadjoint orbits, etc..- 3 Classical r-matrices and Lax equations.- 4 Classical Yang-Baxter identity.- 5 A finite-dimensional example.- 6 Loop algebras and the Riemann problem.- 7 More examples.- 8 Zero curvature equations.- 9 Difference equations and Poisson-Lie groups.- Acknowledgements.- References.- Programme of the Summer School on Factorization and Integrable Systems.
Inhaltsverzeichnis
An Overview of Matrix Factorization Theory and Operator Applications.- 0 Introduction.- 1 General theorems.- 2 Factorization in decomposing Banach algebras.- 3 Generalized Lp factorization.- 4 State space method.- References.- Matrix Riemann-Hilbert Problems Related to Branched Coverings of ??1.- 1 Introduction.- 2 Riemann-Hilbert problem with quasi-permutation monodromies and algebraic curves.- 3 Riemann surfaces. Rauch variational formulas.- 4 Solution of Riemann-Hilbert problems with quasi-permutation monodromies and Szegö kernel.- 5 Isomonodromic tau-function and Cauchy-Riemann determinants.- Acknowledgements.- References.- Quantum Groups and Integrable Models.- 1 Introduction.- 2 Algebraic Bethe Ansatz and QISM.- 3 Yang-Baxter equation.- 4 Thermodynamic limits.- 5 Conclusion.- Acknowledgements.- References.- Integrable Systems and Factorization Problems.- 1 Introduction.- 2 A few preliminaries: Poisson brackets, coadjoint orbits, etc..- 3 Classical r-matrices and Lax equations.- 4 Classical Yang-Baxter identity.- 5 A finite-dimensional example.- 6 Loop algebras and the Riemann problem.- 7 More examples.- 8 Zero curvature equations.- 9 Difference equations and Poisson-Lie groups.- Acknowledgements.- References.- Programme of the Summer School on Factorization and Integrable Systems.
Klappentext
This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.
Expanded lecture notes of a summer school at the University of Algarve, Portugal
Written by leading experts in the field
Extensive review of factorization theory, its application to integrable systems, and its developments over the last 25 years
