Irreducible representations of the quantum Weyl algebra at roots of unity given by matrices

Details Irreducible representations of the quantum Weyl algebra at roots of unity given by matrices Irreducible representations of the quantum Weyl algebra at roots of unity given by matrices

2012-03-08

arxiv.org/abs/1203.1959v1

Mathematics

Representation Theory

5 pages, no figures

Scientific paper

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

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