Geometry of orbits spaces of irreducible representations of Coxeter groups

Irreducible linear representations of a Coxeter group correspond to conjugacy classes of the group. It is known that the orbits spaces of linear representations of Coxeter groups as reflection groups carry a natural structure of polynomial Frobenius manifolds. The aim of this project is to obtain formal construction of Frobenius manifolds or their generalization on the orbit spaces of all irreducible linear representations of Coxeter groups.