Costratified Hilbert space structure for lattice gauge models

The reduced phase space of a system with symmetries, like e.g. gauge theory, is stratified by orbit types. To examine hypothetical quantum effects of the stratification, one has to construct the associated costratification of the Hilbert space of the corresponding quantum theory, proposed by Huebschmann. The method is explained for the adjoint quotient of SU(2), which can be interpreted as SU(2)-lattice gauge theory on a single plaquette, and attempts to generalize it to larger lattices and larger gauge groups are discussed.