We consider the complete normal field net with compact symmetry group
constructed by Doplicher and Roberts starting from a net of local observables
in >=2+1 spacetime dimensions and its set of localized (DHR) representations.
We prove that the field net does not possess nontrivial DHR sectors, provided
the observables have only finitely many sectors. Whereas the superselection
structure in 1+1 dimensions typically does not arise from a group, the DR
construction is applicable to `degenerate sectors', the existence of which (in
the rational case) is equivalent to non-invertibility of Verlinde's S-matrix.
We prove Rehren's conjecture that the enlarged theory is non-degenerate, which
implies that every degenerate theory is an `orbifold' theory. Thus, the
symmetry of a generic model `factorizes' into a group part and a pure quantum
part which still must be clarified.Comment: latex2e, 24 pages. Final version, to appear in Ann. Inst. H. Poinc.
(Theor. Phys.). A serious gap in the proof of Prop. 2.3 has been filled in,
but only under a rationality assumption. The main application to rational
CQFTs is not affected, in fact strenghtened by the new Props. 3.8 and 3.14.
Some remarks have been adde
