Harmonic Maps, Loop Groups, and Integrable Systems

Table of Contents

Preface
Acknowledgements
Part I. One-Dimensional Integrable Systems:
1. Lie groups
2. Lie algebras
3. Factorizations and homogeneous spaces
4. Hamilton's equations and Hamiltonian systems
5. Lax equations
6. Adler-Kostant-Symes
7. Adler-Kostant-Symes (continued)
8. Concluding remarks on one-dimensional Lax equations
Part II. Two-Dimensional Integrable Systems:
9. Zero-curvature equations
10. Some solutions of zero-curvature equations
11. Loop groups and loop algebras
12. Factorizations and homogeneous spaces
13. The two-dimensional Toda lattice
14. T-functions and the Bruhat decomposition
15. Solutions of the two-dimensional Toda lattice
16. Harmonic maps from C to a Lie group G
17. Harmonic maps from C to a Lie group (continued)
18. Harmonic maps from C to a symmetric space
19. Harmonic maps from C to a symmetric space (continued)
20. Application: harmonic maps from S2 to CPn
21. Primitive maps
22. Weierstrass formulae for harmonic maps
Part III. One-Dimensional and Two-Dimensional Integrable Systems:
23. From 2 Lax equations to 1 zero-curvature equation
24. Harmonic maps of finite type
25. Application: harmonic maps from T2 to S2
26. Epilogue
References
Index.

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