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

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 $w_{\infty }^C$-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.

29 pages, published version

References in corpus (2)

• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• From Additional Symmetries to Linearization of Virasoro Symmetries

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• The "ghost" symmetry in the CKP hierarchy
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• Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model
• Toda lattice with constraint of type B
• Kadomtsev-Petviashvili hierarchies of types B and C
• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations