Quantum Galois correspondence for subfactors

Ocneanu has obtained a certain type of quantized Galois correspondence for the Jones subfactors of type A, and his arguments are quite general. By mak ing use of them in a more general context, we define a notion of a subequiv alent paragroup and establish a bijective correspondence between generalize d intermediate subfactors in the sense of Ocneanu and subequivalent paragro ups for a given strongly amenable subfactors of type II, in the sense of Po ps, by encoding the subequivalence in terms of a commuting square. For this encoding, we generalize Sate's construction of equivalent subfactors of fi nite depth from a single commuting square, to strongly amenable subfactors. We also explain a relation between our notion of subequivalent paragroups and sublattices of a Popa system, using open string bimodules. (C) 1999 Aca demic Press.