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

Zhengwei Liu Vanderbilt University, Nashville, USA Scott Morrison Mathematical Sciences Institute, Australian National University, Canberra, Australia David Penneys University of California, Los Angeles, USA

Quantum Algebra Spectral Theory and Operator Algebra mathscidoc:2206.29001

Communications in Mathematical Physics, 334, 889–922, 2014.9
An irreducible II_1-subfactor A⊂B is exactly 1-supertransitive if B⊖A is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index 3+\sqrt{5} ≈ 5.23. 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 (3+\sqrt{5},6+1/5], all with index 3+2\sqrt{2}. 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’.
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  title={1-Supertransitive Subfactors with Index at Most 6+1/5},
  author={Zhengwei Liu, Scott Morrison, and David Penneys},
  booktitle={Communications in Mathematical Physics},
Zhengwei Liu, Scott Morrison, and David Penneys. 1-Supertransitive Subfactors with Index at Most 6+1/5. 2014. Vol. 334. In Communications in Mathematical Physics. pp.889–922. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626170911162062471.
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