#### Alladi Ramakrishnan Hall

#### Angle between intermediate subfactors.

#### Keshab Chandra Bakshi

##### CMI

*We introduce a new notion of angle between intermediate*

subfactors and show that it only takes values (strictly) between 60

and 90 degrees for minimal intermediate subfactors of a finite index

irreducible subfactor. From this rigidity we can bound the number of

minimal intermediate subfactors using an elementary estimate on

kissing numbers in geometry. As a consequence, we improve the existing

upper bound of the cardinality of the set of all intermediate subfactors

thereby answering a question of R. Longo published in 2003. This is joint

work with S. Das, Z. Liu and Y. Ren.

Done