In conformally invariant quantum field theories one encounters besides the standard DHR superselection theory based on spacelike (Einstein-causal) commutation relations and their Haag duality another timelike (''Huygens'') based superselection structure. Whereas the DHR theory based on spacelike causality of observables confirmed the Lagrangian internal symmetry picture on the level of the physical principles of local quantum physics, the attempts to understand the timelike based superselection charges (associated with the center of the conformal covering group) in terms of timelike localized charges lead to a more dynamical role of charges outside the DR theorem and even outside the Coleman-Mandula setting. The ensuing plektonic timelike structure of conformal theories explains the spectrum of the anomalous scale dimensions in terms of phase factors in admissable braid group representations, similar to the explanation of the possible anomalous spin spectrum expected from stringlike d=1+2 fields with braid group statistics.