Abstract

We determine the subfactors N ⊂ R of the hyperfinite II₁-factor R with finite index for which the C^*-tensor category of the associated (N,N)-bimodules is equivalent to the C^*-tensor category U_g 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^G ⊂ (R × L(C^r))^H, where R^G is the fixed point algebra under an outer action α of G, H is a subgroup of G, ψ : H→U(C^r) is a unitary finite dimensional projective representation of H satisfying a certain additional condition and (R × L(C^r))^H is the fixed point algebra under the action α|H × Adψ of H on R × L(C^r).

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