A group-theoretical study of the stabilizer of a generic connection (Q1074872)

Let G be a connected compact simply connected Lie group and let Z(G) be its center. An irreducible connection in a principal bundle over a differentiable manifold \(M^ n\) with G as structure group is a connection A whose holonomy group H(A) does coincide with G. A generic connection A is a connection such that the centralizer \(Z^ G(H(A))\) of H(A) in G is discrete. The authors determine all groups G that do not contain discrete centralizers larger than Z(G). Then they obtain stabilizers of the generic connections in the cases where \(G=Spin(n)\) or \(G=Sp(m)\).