  In this paper, we show that general homogeneous manifolds $G/P$ satisfy
Conjecture $\mathcal{O}$ of Galkin, Golyshev and Iritani which `underlies'
Gamma conjectures I and II of them. Our main tools are the quantum Chevalley
formula for $G/P$ and a theory on nonnegative matrices including
Perron-Frobenius theorem.
