Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895130 | Journal of Geometry and Physics | 2008 | 9 Pages |
Abstract
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 (1+1 wave maps) from surfaces into compact symmetric spaces. An “Iwasawa-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.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
David Brander,