Partial ordering of gauge orbit types for SU(n) gauge theories

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space–time dimension d≤4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space–time, derived earlier, is used. It is shown that on the level of these cohomology elements, the partial ordering relation is characterized by a system of algebraic equations. Moreover, operations to generate direct successors and direct predecessors are formulated. The latter allow to successively reconstruct the set of orbit types, starting from the principal type.