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We consider Kaehler quantized models whose underlying classical phase spacehas a stratified structure induced from the Hamiltonian action of a compact Liegroup. We show how to implement the classical stratification on the level ofthe C*-algebra of observables and discuss the relation to the costratification(in the sense of Huebschmann) of the physical Hilbert space. Our analysis isbased on the T-procedure as developed by Grundling and Hurst. We apply thegeneral theory to Yang-Mills theory on a finite lattice, where thestratification is given by the classical gauge orbit types.

Stratified structure of the observable algebra of Hamiltonian lattice gauge theory