Irreducible Representations of the Quantum Weyl Algebra at Roots of Unity Given by Matrices

To describe the representation theory of the quantum Weyl algebra at an lth primitive root γ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation yx ? γxy = 1, assuming yx ≠ xy. In this note, we complete their result by finding and classifying, up to equivalence, all irreducible matrix solutions (X, Y), where X is singular.