Generators for Rational Loop Groups and Geometric Applications
Differential Geometry
2008-03-04 v1
Abstract
Uhlenbeck proved that a set of simple elements generates the group of rational loops in GL(n,C) that satisfy the U(n)-reality condition. For an arbitrary complex reductive group, a choice of representation defines a notion of rationality and enables us to write down a natural set of simple elements. Using these simple elements we prove generator theorems for the fundamental representations of the remaining neo-classical groups and most of their symmetric spaces. In order to apply our theorems to submanifold geometry we also obtain explicit dressing and permutability formulae. We introduce a new submanifold geometry associated to G_2/SO(4) to which our theory applies.
Cite
@article{arxiv.0803.0029,
title = {Generators for Rational Loop Groups and Geometric Applications},
author = {Neil Donaldson and Daniel Fox and Oliver Goertsches},
journal= {arXiv preprint arXiv:0803.0029},
year = {2008}
}