Fixed point resolution in extensions of permutation orbifolds

We determine the simple currents and fixed points of the orbifold theory CFT⊗CFT/Z2, given the simple currents and fixed point of the original CFT. We see in detail how this works for the SU(2)k WZW model, focusing on the field content (i.e. h-spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the SJ matrices associated to each simple current for SU(2)2 and for the B(n)1 and D(n)1 series.