Irreducible subfactors of $L({\mathbb{F}}_{\infty })$ of index $\lambda >4$

Abstract

By utilizing an irreducible inclusion of type III${}_{q^2}$ factors coming from a free-product type action of the quantum group $S{U}_q(2)$, we show that the free group factor $L({\mathbb{F}}_{\infty })$ possesses irreducible subfactors of arbitrary index $>4$. Combined with earlier results of Radulescu, this shows that $L({\mathbb{F}}_{\infty })$ has irreducible subfactors with any index value in $\{4{\cos }^2(\pi /n):n\ge 3\}\cup [4,+\infty )$.

Final version (correcting typos and adding an appendix)