CONTINUOUS FAMILIES OF HYPERFINITE SUBFACTORS WITH THE SAME STANDARD INVARIANT

Abstract

We construct numerous continuous families of irreducible subfactors of the hyperfinite II1 factor which are non-isomorphic, but have all the same standard invariant. In particular, we obtain 1-parameter families of irreducible, non-isomorphic subfactors of the hyperfinite II1 factor with Jones index 6, which have all the same standard invariant with property (T). We exploit the fact that property (T) groups have uncountably many non-cocycle conjugate cocycle actions on the hyperfinite II1 factor.