%0 Journal Article
%T Loop groups and holomorphic bundles
%A Jacques C. Hurtubise
%A Michael K. Murray
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0812.3684v1