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

Defining relations for the orbit type strata of SU(2)-lattice gauge models