Conjugate connections and moduli spaces of connections (Q1365392)

Let \(G\) be a Lie group and \(H\) a closed subgroup, where \(\Aut(G,H)\) is the group of automorphisms of \(G\) leaving all elements of \(H\) fixed, and \(\text{Inn}(G, H)\) its normal subgroup consisting of inner automorphisms. Given a principal \(G\)-bundle \(P\), let \({\mathcal C}(P)\) be the space of connections in \(P\) and \({\mathcal G}(P)\) the group of gauge transformations. The paper shows that, if the structure group \(G\) of \(P\) can be reduced to \(H\), then the group \(\Aut(G, H)/\text{Inn}(G, H)\) acts on the moduli space \({\mathcal C}(P)/{\mathcal G}(P)\), and the action is free on the generic part of \({\mathcal C}(P)/{\mathcal G}(P)\).