Generating rational loop groups with noncompact reality conditions
Differential Geometry
2018-03-16 v3
Abstract
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).
Cite
@article{arxiv.0910.1687,
title = {Generating rational loop groups with noncompact reality conditions},
author = {Oliver Goertsches},
journal= {arXiv preprint arXiv:0910.1687},
year = {2018}
}
Comments
15 pages. In v1 and v2 (identical by mistake) the generating theorem for loops satisfying the U(p,q)-reality condition contained a gap. v3: published version