ORBIFOLD SUBFACTORS FROM HECKE ALGEBRAS II - QUANTUM DOUBLES AND BRAIDING

A. Ocneanu has observed that a mysterious orbifold phenomenon occurs i n the system of the M-infinity-M-infinity bimodules of the asymptotic inclusion, a subfactor analogue of the quantum double, of the Jones su bfactor of type A(2n+1).We show that this is a general phenomenon and identify some of his orbifolds with the ones in our sense as subfactor s given as simultaneous fixed point algebras by working on the Hecke a lgebra subfactors of type A of Wenzl. That is, we work on their asympt otic inclusions and show that the M-infinity-M-infinity bimodules are described by certain orbifolds (with ghosts) for SU(3)(3k). We actuall y compute several examples of the (dual) principal graphs of the asymp totic inclusions. As a corollary of the identification of Ocneanu's or bifolds with ours, we show that a non-degenerate braiding exists on th e even vertices of D-2n, n > 2.