Tau function of the CKP hierarchy and nonlinearizable Virasoro symmetries (Q2852523)

It is known that the tau function may be constructed from the action of bosonic fields on the vacuum vector in Fock space. In this paper, the authors introduce a tau function of the CKP hierarchy by making use of its Hamiltonian densities and considering the fact that the hierarchy carries a series of bi-Hamiltonian structures reduced from those for the KP hierarchy. They study the action on it by the additional symmetries of the CKP hierarchy which implies not only a central extension of the algebra but also some non-trivial ``tails'' given by polynomials in at least second-order derivatives of the \(\log\) tau function with respect to the time variables. The paper is also motivated by the study of nonlinearizable Virasoro symmetries for integrable hierarchies when considering Drinfeld-Sokolov hierarchies associated to affine Kac-Moody-algebras of type C and hence proves that the Virasoro symmetries are nonlinearizable when acting on the tau function.