Generators for rational loop groups

DOI10.1090/S0002-9947-2011-05120-2zbMath1226.22025arXiv0803.0029OpenAlexW2049689344MaRDI QIDQ5200196

Oliver Goertsches, Daniel Fox, Neil M. Donaldson

Publication date: 1 August 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0029

zbMATH Keywords

loop groupintegrable system\(G_2\)dressing actiontwisted loop groupgenerator theoremsubmanifold geometrysimple elementrational loop

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Differential geometry of symmetric spaces (53C35)

Related Items (5)

PROJECTIVE LOOPS GENERATE RATIONAL LOOP GROUPS ⋮ Darboux transformation for nonlinear Schrödinger type hierarchies ⋮ Loop group decompositions in almost split real forms and applications to soliton theory and geometry ⋮ Bianchi-Bäcklund transforms and dressing actions, revisited ⋮ Solitons for the Schrödinger flows on Hermitian symmetric spaces

Cites Work

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• Conformally flat submanifolds in spheres and integrable systems
• Bäcklund transformations, Ward solitons, and unitons
• Transformations of flat Lagrangian immersions and Egoroff nets
• Calibrated geometries
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Soliton equations and differential geometry
• Harmonic two-spheres in compact symmetric spaces, revisited
• Isometric immersions of space forms and soliton theory
• The submanifold geometries associated to Grassmannian systems
• Bäcklund transformations and loop group actions

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