Q-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformations
arXiv:solv-int/9811010
Abstract
We study the additional symmetries associated with the -deformed Kadomtsev-Petviashvili (-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the -KP hierarchy can be consistently reduced to the so-called -deformed constrained KP (-cKP) hierarchy. We then show that the additional symmetries acting on the wave function can be viewed as infinitesimal Bäcklund transformations by acting the vertex operator on the tau-function of the -KP hierarchy. This establishes the Adler-Shiota-van Moerbeke formula for the -KP hierarchy.
9 pages, Revtex, no figures