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Classifying irreducible finite-dimensional representations of the $q$-Weyl algebra

I have that $A = \langle x, y : yx = qxy \rangle$ is the $q$-Weyl algebra, with basis $x^iy^j$, $i, j \in \mathbb{Z}$. The base field is $\mathbb{C}$. I need to classify the irreducible finite-dimensional representations. Assuming $V$ is such a module, I have shown that $\{v, xv, \dots, x^{m-1}v\}$ is a basis, where […]

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Ask Mathematics

Classifying irreducible finite-dimensional representations of the $q$-Weyl algebra

I have that $A = \langle x, y : yx = qxy \rangle$ is the $q$-Weyl algebra, with basis $x^iy^j$, $i, j \in \mathbb{Z}$. The base field is $\mathbb{C}$. I need to classify the irreducible finite-dimensional representations. Assuming $V$ is such a module, I have shown that $\{v, xv, \dots, x^{m-1}v\}$ is a basis, where […]