  We review the framework subfactors provide for understanding modular
invariants. We discuss the structure of a generalized Longo-Rehren subfactor
and the relationship between the coupling matrices of such subfactors, modular
invariance and local extensions. We relate results of Kostant, in the context
of the McKay correspondence for finite subgroups of SU(2), to subfactors. A
direct proof of how alpha-induction produces modular invariants is presented.
