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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 .
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Samuel A. Lopes, João N.P. Lourenço, A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra. Port. Math. 72 (2015), no. 4, pp. 407–419DOI 10.4171/PM/1973