2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157431In this paper, we construct families of irreducible representations for a class of quantum groups $U_{q}(f_{m}(K))$. First, we give a natural construction of irreducible weight representations for $U_{q}(f_{m}(K))$ using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of $U_{q}(f_{m}(K))$. As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.19 pages, some modifications made to the first versionRepresentation Theory17B37, 16B30, 16B35text