Frobenius manifolds for l-Kronecker quivers

For finite or affine root systems, there is a construction of Frobenius manifolds associated with the invariant theory of their Weyl groups. On the other hand, for indefinite type root systems, it is not known whether there is a natural construction of Frobenius manifolds associated with them. In this talk, as a partial answer for the question, we give a construction for the simplest case, which is the indefinite root system of rank two arising from the l-Kronecker quiver. This is a joint work with T.Otani, Y.Shiraishi, and A.Takahashi.