  We parameterize the finite-dimensional irreducible representations of a class
of pointed Hopf algebras over an algebraically closed field of characteristic
zero by dominant characters. The Hopf algebras we are considering arise in the
work of N. Andruskiewitsch and the second author. Special cases are the
multiparameter deformations of the enveloping algebras of semisimple Lie
algebras where the deforming parameters are not roots of unity and some of
their finite-dimensional versions in the root of unity case.
