II1-subfactors associated with the C∗-tensor category of a finite group

Abstract

We determine the subfactors N ⊂ R of the hyperfinite II1factor R with finite index for which the C∗-tensor category of the associated (N,N)-bimodules is equivalent to the C∗-tensor category UG of all unitary finite dimensional representations of a given finite group G. It turns out that every subfactor of that kind is isomorphic to a subfactor R ⊂ (R ⊗ L(C)) , where R is the fixed point algebra under an outer action α of G, H is a subgroup of G, ψ : H −→ U(C) is a unitary finite dimensional projective representation of H satisfying a certain additional condition and (R⊗L(Cr))H is the fixed point algebra under the action α |H ⊗Adψ of H on R⊗ L(C).