A Galois correspondence for compact quantum group actions

We establish a Galois correspondence for a minimal action of a compact quantum group ${\mathbb G}$ on a von Neumann factor $M$. This extends the result of Izumi, Longo and Popa who treated the case of a Kac algebra. Namely, there exists a one-to-one correspondence between the lattice of left coideals of ${\mathbb G}$ and that of intermediate subfactors of $M^{\mathbb G}\subset M$.