Planar algebras and the ocneanu-szymanski theorem

Das, Paramita ; Kodiyalam, Vijay (2005) Planar algebras and the ocneanu-szymanski theorem Proceedings of the American Mathematical Society, 133 (09). pp. 2751-2759. ISSN 0002-9939

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We give a very simple 'planar algebra' proof of the part of the Ocneanu-Szymanski theorem which asserts that for a finite index, depth two, irreducible II1-subfactor N⊂M, the relative commutants N'∩M1 and M'∩M2 admit mutually dual Kac algebra structures. In the hyperfinite case, the same techniques also prove the other part, which asserts that N'∩M1 acts on M with invariants N.

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