  We give three applications of general theory about braided endomorphisms from
conformal inclusions developed previously by us. The first is an example of
subfactors associated with conformal inclusion whose dual fusion ring is
non-commutative. In the second application we show that the Kac-Wakimoto
hypothesis about certain relations between branching rules and S-matrices,
which has existed for almost a decade, is not true in at least three examples.
Finally we show that the fusion rings of subfactors associated with the
conformal inclusions $SU(n)_{(n+2)}\subset SU(n(n+1)/2)$ and $SU(n+2)_n\subset
SU((n+1)(n+2)/2)$ are canonically isomorphic using a version of level-rank
duality.
