  This paper considers the links between the geometry of the various flag
manifolds of loop groups and bundles over families of rational curves. Aa an
application, a stability result for the moduli on a rational ruled surface of
G-bundles with additional flag structure along a line is proven for any
reductive group; this gives the corresponding stability statement for any
compact group K for the moduli of K-instantons over the four-sphere, and for
the moduli of K-calorons over the three-sphere times the circle. The paper also
considers the Hecke transforms on bundles induced by outer automorphisms of the
loop groups.
