Narrow Results

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.