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 $M^{ \mathbb G}\subset M$.
Categories: math.OA