  In 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.
