Generators for Rational Loop Groups and Geometric Applications
| dc.creator | Donaldson, Neil | |
| dc.creator | Fox, Daniel | |
| dc.creator | Goertsches, Oliver | |
| dc.date | 2008-03-01 | |
| dc.date.accessioned | 2026-07-07T09:24:14Z | |
| dc.date.available | 2026-07-07T09:24:14Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0803.0029 | |
| dc.identifier | http://arxiv.org/abs/0803.0029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156023 | |
| dc.subject | Differential Geometry | |
| dc.title | Generators for Rational Loop Groups and Geometric Applications | |
| dc.type | text |