Ergodic actions of S_mu U(2) on C*-algebras from II_1 subfactors

To a proper inclusion N subset of M of II1 factors of finite Jones index [M : N ], we associate an ergodic C*-action of the quantum group S mu U(2) (or more generally of certain groups A(0)(F)). The higher relative commutant N' boolean AND Mr-1 can be identified with the spectral space of the rth tensor power u(circle times r) of the defining representation Of the quantum group. The index and the deformation parameter are related by - 1 <= mu < 0 and [M : N] = vertical bar mu + mu(-1)vertical bar. This ergodic action may be thought of as a virtual Subgroup of S,,U(2) in the sense of Mackey arising from the tensor category generated by the N-bimodule M-N(N). mu is negative as M-N(N) is a real bimodule. (C) 2009 Elsevier B.V. All rights reserved.