Harmonic maps into Lie groups: classical solutions of the chiral model

PART 1 2 1. Basic formulas and characteristic notation 2 2. The canonical associated linear problem or Lax pair 5 3. The Dolan representation 8 4. The variation formulas for the extended solution 12 5. The representation of $/ (S 2 , G) on holomorphic maps C* - G 14 6. The representation of J#k(S 2 , G) on extended harmonic maps and Backlund transformations 20 7. The additional S action 23 8. Harmonic maps into Grassmannians 24 PART II 27 9. The single uniton 27 10. The fixed points of the S action 31 11. Global conservation laws and finiteness 35 12. Adding a uniton by singular Backlund transformation 37 13. The minimal uniton number 40 14. The unique factorization theorem 42 15. Complex Grassmannian manifolds again 45 16. Additional questions and problems 47