On the conjecture OO of GGI for G/P

In this paper, we show that general homogeneous manifolds G/PG/P satisfy Conjecture OO of Galkin, Golyshev and Iritani which ‘underlies’ Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for G/PG/P and a theory on nonnegative matrices including Perron–Frobenius theorem.