Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro symmetries

TL;DR

This paper proves that tau-symmetric bihamiltonian deformations of the Principal Hierarchy's tau-cover for semisimple Frobenius manifolds possess an infinite set of Virasoro symmetries, revealing deep symmetry structures.

Contribution

It establishes the existence of Virasoro symmetries in deformed tau-covers of Principal Hierarchies for semisimple Frobenius manifolds, extending previous understanding.

Findings

Infinite Virasoro symmetries exist in deformed tau-covers

Results apply to tau-symmetric bihamiltonian deformations

Enhances understanding of symmetry structures in integrable hierarchies

Abstract

We prove that for any tau-symmetric bihamiltonian deformation of the tau-cover of the Principal Hierarchy associated with a semisimple Frobenius manifold, the deformed tau-cover admits an infinite set of Virasoro symmetries.