Multi-Sided Braid Type Subfactors, II

Abstract

AbstractWe show that the multi-sided inclusion R⊗l ⊂ R of braid-type subfactors of the hyperfinite II1 factor R, introduced in Multi-sided braid type subfactors [E3], contains a sequence of intermediate subfactors: R⊗l ⊂ R⊗l−1 ⊂ … ⊂ R⊗2 ⊂ R. That is, every t-sided subfactor is an intermediate subfactor for the inclusion R⊗l ⊂ R, for 2 ≤ t ≤ l. Moreover, we also show that if t > m then R⊗t ⊂ R⊗m is conjugate to R⊗t−m+1 ⊂ R. Thus, if the braid representation considered is associated to one of the classical Lie algebras then the asymptotic inclusions for the Jones-Wenzl subfactors are intermediate subfactors.