$II_1$-Subfactors associated with the $C^*$-Tensor Category of a Finite Group

Abstract

We determine the subfactors $N\subset R$ of the hyperfinite $II_1$-factor R with finite index for which the $C^*$-tensor category of the associated $(N,N)$-bimodules is equivalent to the $C^*$-tensor category $\C{U}_G$ of all unitary finite dimensional representations of a given finite group G.