  We study inclusions of local, chiral, conformal quantum theories C which are
contained in an ambient theory B and commute with another given subtheory A.
These subtheories C are called Coset models. Most of our results are
model-independent, although our analysis is motivated by the inclusions of
current algebras and their Coset models.
  We prove that to every given A contained in B there is a unique, inner
representation U^A which implements conformal symmetry on the subnet. The local
observables of B which commute with U^A form the maximal Coset model C_max.
Assuming U^A to be generated by integrals of a quantum field affiliated with
the subnet A, we show: The inclusion of the subnet and of its Coset models is
directly analogous to the inclusion of chiral observables in a local, conformal
theory in 1+1 dimensions. The local observables of the maximal Coset model
associated with a given region are found to be characterised by their commuting
with the local observables of A associated with the very same region. We give
applications and discuss possible generalisations of our methods.
