Loop group decompositions in almost split real forms and applications to soliton theory and geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Brander, David

关键词: Differential geometry;    Loop groups;    Integrable systems;    Soliton theory;   

DOI  :  10.1016/j.geomphys.2008.09.003

来源: Elsevier

【 摘 要 】

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action - by the whole subgroup of loops which extend holomorphically to the exterior disc - on the U-hierarchy of the ZS-AKNS systems, on curved flats and on various other integrable systems, is global for compact cases. It also implies a global infinite dimensional Weierstrass-type representation for Lorentzian harmonic maps (I + 1 wave maps) from surfaces into compact symmetric spaces. An lwasawa-type decomposition of the same type of real form, with respect to a fixed point subgroup of an involution of the second kind, is also proved, and an application given. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free