Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries

TL;DR

This paper introduces a tau function for the CKP hierarchy, explores its symmetries, and demonstrates that certain Virasoro symmetries are non-linearizable on the tau function, revealing new algebraic structures.

Contribution

It presents a novel tau function for the CKP hierarchy and analyzes the non-linearizability of Virasoro symmetries in related Drinfeld-Sokolov hierarchies.

Findings

A single tau function for the CKP hierarchy is constructed.

Additional symmetries involve more than a central extension of the $w^C_ Infty$-algebra.

Virasoro symmetries are shown to be non-linearizable on the tau function.

Abstract

We introduce a single tau function that represents the CKP hierarchy into a generalized Hirota "bilinear" equation. The actions on the tau function by additional symmetries for the hierarchy are calculated, which involve strictly more than a central extension of the $w^C_\infty$-algebra. As an application, for Drinfeld-Sokolov hierarchies of type C that are equivalent to certain reductions of the CKP hierarchy, their Virasoro symmetries are proved to be non-linearizable when acting on the tau function.