On the stratified classical configuration space of lattice QCD

The stratified structure of the configuration space GN=G×⋯×G reduced with respect to the action of G by inner automorphisms is investigated for G=SU(3). This is a finite dimensional model coming from lattice QCD. First, the stratification is characterized algebraically, for arbitrary N. Next, the full algebra of invariants is discussed for the cases N=1 and N=2. Finally, for N=1 and N=2, the stratified structure is investigated in some detail, both in terms of invariants and relations and in more geometric terms. Moreover, the strata are characterized explicitly using local cross sections.