  We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this
is a system with symmetries whose configuration space is a direct product of
copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining
relations for the orbit type strata in the reduced classical phase space. The
latter is realized as a certain quotient of a direct product of copies of the
complexified group SL(2,\CC) (sometimes named the GIT-quotient because it
provides a categorical quotient in the sense of geometric invariant theory).
The relations derived can be used for the construction of the orbit type
costratification of the Hilbert space of the quantum system in the sense of
Huebschmann.
