JournalsqtVol. 9, No. 3pp. 473–562

The classification of 3n3^n subfactors and related fusion categories

  • Masaki Izumi

    Kyoto University, Japan
The classification of $3^n$ subfactors and related fusion categories cover

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Abstract

We investigate a (potentially infinite) series of subfactors, called 3n3^n subfactors, including A4A_4, A7A_7, and the Haagerup subfactor as the first three members corresponding to n=1,2,3n=1,2,3. Generalizing our previous work for odd nn, we further develop a Cuntz algebra method to construct 3n3^n subfactors and show that the classification of the 3n3^n subfactors and related fusion categories is reduced to explicit polynomial equations under a mild assumption, which automatically holds for odd nn. In particular, our method with n=4n=4 gives a uniform construction of 44 finite depth subfactors, up to dual, without intermediate subfactors of index 3+53+\sqrt{5}. It also provides a key step for a new construction of the Asaeda–Haagerup subfactor due to Grossman, Snyder, and the author.

Cite this article

Masaki Izumi, The classification of 3n3^n subfactors and related fusion categories. Quantum Topol. 9 (2018), no. 3, pp. 473–562

DOI 10.4171/QT/113