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We construct global observable algebras and global DHR morphisms for theVirasoro minimal models with central charge c(2,q), q odd. To this end, we pass{}from the irreducible highest weight modules to path representations, whichinvolve fusion graphs of the c(2,q) models. The paths have an interpretation interms of quasi-particles which capture some structure of non-conformalperturbations of the c(2,q) models. The path algebras associated to the pathspaces serve as algebras of bounded observables. Global morphisms whichimplement the superselection sectors are constructed using quantum symmetries:We argue that there is a canonical semi-simple quantum symmetry algebra foreach quasi-rational CFT, in particular for the c(2,q) models. These symmetryalgebras act naturally on the path spaces, which allows to define a globalfield algebra and covariant multiplets therein.Comment: 50 pages, Plain TeX, 2 figure

From Path Representations to Global Morphisms for a Class of Minimal Models