Gauge orbit types for theories with gauge group \(O(n)\), \(SO(n)\) or \(Sp(n)\) (Q532490)

The authors determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group \(O(n)\), \(SO(n)\) or \(Sp(n)\) over a closed, simply connected manifold of dimension 4. Complemented with earlier results on \(U(n)\) and \(SU(n)\) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way the authors derive the classification of principal bundles with structure group \(SO(n\)) over these manifolds and the Howe subgroups of \(SO(n)\).