A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra

Abstract

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.

12 pages, Section 2 has been reorganized, new material added in a new Section 3