1-Supertransitive Subfactors with Index at Most 6 1/5

Abstract

An irreducible II1-subfactor (Formula presented.) is exactly 1-supertransitive if (Formula presented.) is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most (Formula presented.), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index (Formula presented.). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier. There are exactly three such subfactors with index in (Formula presented.), all with index (Formula presented.). One of these comes from SO(3)q at a root of unity, while the other two appear to be closely related, and are ‘braided up to a sign’. This is the published version of arXiv:1310.8566.