Algebraic classical W-algebras and Frobenius manifolds

We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space common equilibrium points defined by its leading term. On this space, we construct local which forms an exact Poisson pencil, defines algebraic classical W-algebra, admits dispersionless limit, term Frobenius manifold. This leads to uniform construction manifolds corresponding regular cuspidal conjugacy classes in irreducible Weyl groups.