  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.
