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For any semisimple Frobenius manifold, we prove that a tau-symmetricbihamiltonian deformation of its Principal Hierarchy admits an infinite familyof linearizable Virasoro symmetries if and only if all the central invariantsof the corresponding deformation of the bihamiltonian structure are equal to$\frac{1}{24}$. As an important application of this result, we prove that theDubrovin-Zhang hierarchy associated with the semisimple Frobenius manifoldpossesses a bihamiltonian structure which can be represented in terms ofdifferential polynomials.

Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds