Representations of pointed Hopf algebras and their Drinfel'd quantum doubles

We study representations of nontrivial liftings of nilpotent type of quantum linear spaces and their Drinfel'd quantum doubles. We construct a family of Verma-type modules in both cases and prove a parametrization theorem for simple modules. We compute the Loewy and socle series of Verma modules under a mild restriction on the datum of a lifting. We find bases and dimensions of simple modules. (C) 2009 Elsevier Inc. All rights reserved.