Integrable hierarchies associated to infinite families of Frobenius manifolds
We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to AN, DN and BN singularities. In the case of AN Frobenius manifolds our hierarchy turns out to coincide with the KP hierarchy; for BN Frobenius manifolds it coincides with the BKP hierarchy; and for DN hierarchy it is a certain reduction of the 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of AN, DN and BN Frobenius potentials.