Around 1980's Kyoji Saito, Yano and Sekiguchi showed the existence of the flat coordinates on the orbit spaces of coxeter groups. Later, their result was formulated and generalized by Dubrovn in terms of the theory of Frobenius manifold and its almost duality.

In 2015, Kato, Mano and Sekiguchi showed the existence of flat structures for duality groups. ( A duality group is an irreducible,well-generated finite complex reflection group.) In this talk, I will explain how to characterize their flat structure from the viewpoint of almost duality. The talk is based on the joint work with Satoshi Minabe and Yuuki Shiraishi.