The representation category of any compact group is the bimodule category of a II_1 factor

Abstract

We prove that given any compact group G, there exists a minimal action of G on a II_1 factor M such that the bimodule category of the fixed-point II_1 factor M^G is naturally equivalent with the representation category of G. In particular, all subfactors of M^G with finite Jones index can be described explicitly.

v4:Improved and more detailed exposition. No conceptual changes. Final version. v3:Correction to a technical assumption; clarification of corresponding proof. v2:Update and correction of references