A multiparameter family of irreducible representations of the quantum   plane and of the quantum Weyl algebra
  We construct a family of irreducible representations of the quantum plane and of the quantum Weyl algebra over an arbitrary field, assuming the deformation parameter is not a root of unity. We determine when two representations in this family are isomorphic, and when they are weight representations, in the sense of Bavula. 
Samuel A. Lopes and Jo\~ao N. P. Louren\c{c}o
math.RT