Irreducible subfactors of $L(\mathbb F_\infty)$ of index $\lambda \gt 4$
Dimitri Shlyakhtenko and Yoshimichi Ueda
By utilizing an irreducible inclusion of type III$ _{q^{2}} $ factors coming from a free-product type action of the quantum group $ SU_{q}(2) $, we show that the free group factor $ L(\mathbb {F}_{\infty }) $ possesses irreducible subfactors of arbitrary index $ \gt 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\geq 3\}\cup [4,+\infty ) $.