Orbifold subfactors from Hecke algebras II - Quantum doubles and braiding

A. Ocneanu has observed that a mysterious orbifold phenomenon occurs in the system of the M-infinity-M-infinity bimodules of the asymptotic inclusion, a subfactor analogue of the quantum double, of the Jones subfactor 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 subfactors given as simultaneous fixed point algebras by working on the Hecke algebra subfactors of type A of Wenzl. That is, we work on their asymptotic inclusions and show that the M-infinity-M-infinity bimodules are described by certain orbifolds (with ghosts) for SU(3)(3k). We actually compute several examples of the (dual) principal graphs of the asymptotic inclusions. As a corollary of the identification of Ocneanu's orbifolds with ours, we show that a non-degenerate braiding exists on the even vertices of D-2n, n > 2.