An angle between intermediate subfactors and its rigidity

Keshab Chandra Bakshi Institute of Mathematical Science, Homi Bhabha National Institute, Chennai, India Sayan Das Department of Mathematics, University of Iowa, Iowa City IA 52242 Zhengwei Liu Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Yunxiang Ren Department of Mathematics, University of Tennessee, Knoxville TN 37996

Quantum Algebra mathscidoc:2207.29001

Transactions of the American Mathematical Society, 371, 5973-5991, 2018.12
We introduce a new notion of an angle between intermediate subfactors and prove various interesting properties of the angle and relate it to the Jones index. We prove a uniform 60 to 90 degree bound for the angle between minimal intermediate subfactors of a finite index irreducible subfactor. From this rigidity we can bound the number of minimal (or maximal) intermediate subfactors by the kissing number in geometry. As a consequence, the number of intermediate subfactors of an irreducible subfactor has at most exponential growth with respect to the Jones index. This answers a question of Longo’s published in 2003.
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@inproceedings{keshab2018an,
  title={An angle between intermediate subfactors and its rigidity},
  author={Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, and Yunxiang Ren},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703160247569804534},
  booktitle={Transactions of the American Mathematical Society},
  volume={371},
  pages={5973-5991},
  year={2018},
}
Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, and Yunxiang Ren. An angle between intermediate subfactors and its rigidity. 2018. Vol. 371. In Transactions of the American Mathematical Society. pp.5973-5991. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703160247569804534.
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