Commuting-Square Subfactors and Central Sequences

Abstract

Let $M_0\subset M_1$ be a finite-index infinite-depth hyperfinite $I{I}_1$ subfactor and $\omega$ a free ultrafilter of the natural numbers. We show that if this subfactor is constructed from a commuting square then the central sequence inclusion $M_0^{\omega }\cap M_1^{\prime }\subset (M_0{)}_{\omega }$ has infinite Pimnser-Popa index. We will also demonstrate this result for certain infinite-depth hyperfinite subfactors coming from groups.

18 pages