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arXiv · 1710.00285

An angle between intermediate subfactors and its rigidity

Keshab Chandra Bakshi·Sayan Das·Zhengwei Liu·Yunxiang Ren
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Abstract

We introduce a new notion of angle between intermediate subfactors and prove various interesting properties of the angle and relate it with 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 intermediate subfactors of an irreducible subfactor has at most exponential growth with respect to the Jones index. This answers a question of Longo published in 2003.

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Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, Yunxiang Ren. 2017-10-01. An angle between intermediate subfactors and its rigidity. https://arxiv.org/abs/1710.00285

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