Recursion Operators and Frobenius Manifolds

Recursion operators are usually defined, within the theory of bihamiltonian systems, as a special class of tensor fields of type (1,1) with vanishing Nijenhuis torsion. In the talk I enlarge the concept of recursion operator so to encompass a special class of tensor fields of type (1,1) with vanishing Haantjes tensor, and I show that recursion operators in this generalized sense are deeply enrooted in the theory of Frobenius manifolds. In particular, I show how the Saito theory of Frobenius structures on the space of orbits of Coxeter groups can be read from the viewpoint of the theory of recursion operators.