Weak Hopf C∗-algebras and depth two subfactors

We prove that for a finite index and depth two inclusion N⊂M of II1 factors, the relative commutants N′∩M1 and M′∩M2 admit mutually dual weak Hopf C∗-algebra structures. The proof is based on ‘planar algebra techniques’. In the hyperfinite case, one can show that N′∩M1 acts on M with invariants N using this approach.