  Pairs $\aa \subset \bb$ of local quantum field theories are studied, where
$\aa$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral
or two-dimensional. The local correlation functions of fields from $\bb$ have
an expansion with respect to $\aa$ into \cfb s, which are non-local in general.
Two methods of computing characteristic invariant ratios of structure constants
in these expansions are compared: $(a)$ by constructing the monodromy \rep of
the braid group in the space of solutions of the Knizhnik-Zamolodchikov
differential equation, and $(b)$ by an analysis of the local subfactors
associated with the extension with methods from operator algebra (Jones theory)
and algebraic quantum field theory. Both approaches apply also to the reverse
problem: the characterization and (in principle) classification of local
extensions of a given theory.
