Generating rational loop groups with noncompact reality conditions

Details Generating rational loop groups with noncompact reality conditions Generating rational loop groups with noncompact reality conditions

2009-10-09

arxiv.org/abs/0910.1687v2

Mathematics

Differential Geometry

15 pages. the proof in v1 of the generating theorem for loops satisfying the U(p,q)-reality condition contained a gap

Scientific paper

We find generators for the full rational loop group of GL(n,C) as well as for
the subgroup consisting of loops that satisfy the reality condition with
respect to the noncompact real form GL(n,R). We calculate the dressing action
of some of those generators on the positive loop group, and apply this to the
ZS-AKNS flows and the n-dimensional system associated to GL(n,R)/O(n).

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