Q-Deformed KP Hierarchy: Its Additional Symmetries and Infinitesimal Backlund Transformations

摘要

We study the additional symmetries associated with the q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the q-KP hierarchy can be consistently reduced to the so-called q-deformed constrained KP (q-cKP) hierarchy. We then show that the additional symmetries acting on the wave function can be viewed as infinitesimal Backlund transformations by acting the vertex operator on the tau-function of the q-KP hierarchy. This establishes the Adler-Shiota-van Moerbeke formula for the q-KP hierarchy.