2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94469We 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 Bäcklund 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.9 pages, Revtex, no figuresExactly Solvable and Integrable Systemstext