Q-deformed KP hierarchy: Its additional symmetries and infinitesimal backlund transformations

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 cons istently reduced to the so-called q-deformed constrained KP (q-cKP) hierarc hy. We then show that the additional symmetries acting on the wave function can be viewed as infinitesimal Backlund transformations by acting the vert ex operator on the tau-function of the q-KP hierarchy. This establishes the Adler-Shiota-van Moerbeke formula for the q-KP hierarchy.