  Borchers has shown that in a translation covariant vacuum representation of a
theory of local observables with positive energy the following holds: The
(Tomita) modular objects associated with the observable algebra of a fixed
wedge region give rise to a representation of the subgroup of the Poincare
group generated by the boosts and the reflection associated to the wedge, and
the translations. We prove here that Borchers' theorem also holds in charged
sectors with (possibly non-Abelian) braid group statistics in low space-time
dimensions. Our result is a crucial step towards the Bisognano-Wichmann theorem
for Plektons in d=3, namely that the mentioned modular objects generate a
representation of the proper Poincare group, including a CPT operator. Our main
assumptions are Haag duality of the observable algebra, and translation
covariance with positive energy as well as finite statistics of the sector
under consideration.
