IRREDUCIBLE SUBFACTORS OF L(𝔽_{∞}) OF INDEX λ > 4

DIMITRI SHLYAKHTENKO YOSHIMICHI UEDA

Abstract. 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(𝔽_{∞}) possesses irreducible subfactors of arbitrary index > 4. Combined with earlier results of Radulescu, this shows that L(𝔽_{∞}) has irreducible subfactors with any index value in {4 cos^{2}(π/n) : n ≥ 3} ∪ [4, +∞).