Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds

Abstract

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

References in corpus (4)

• Double ramification cycles and integrable hierarchies
• Bi-Hamiltonian recursion, Liu-Pandharipande relations, and vanishing terms of the second Dubrovin-Zhang bracket
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro symmetries
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one

Cited by in corpus (1)

• Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro symmetries