Symmetries of the space of connections on a principal G-bundle and related symplectic structures

There are two groups which act in a natural way on the bundle TP tangent to the total space P of a principal G-bundle P(M,G): the group Aut(0)TP of automorphisms of TP covering the identity map of P and the group TG tangent to the structural group G. Let Aut(TG)TP subset of Aut(0)TP be the subgroup of those automorphisms which commute with the action of TG. In the paper, we investigate G-invariant symplectic structures on the cotangent bundle T*P which are in a one-to-one correspondence with elements of Aut(TG)TP. Since, as it is shown here, the connections on P(M,G) are in a one-to-one correspondence with elements of the normal subgroup Aut(N)TP of Aut(0)TP, so the symplectic structures related to them are also investigated. The Marsden-Weinstein reduction procedure for these symplectic structures is discussed.