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I was looking for a reference on representations of $GL_n(\mathbb{Z}/p^k\mathbb{Z})$ over $\mathbb{F}_p$. In particular what the irreducible and indecomposable representations look like.

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    $\begingroup$ Over $\mathbb{C}$, this problem is open for $n \geq 3$ and $k$ arbitrary. $\endgroup$
    – Peter Humphries
    Commented Sep 7, 2020 at 23:59
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    $\begingroup$ For irreducible representations, it reduces to the case k=1 (where a lot of things are known thank to the theory of polynomial representations, for example, even if the dimensions of the irreducible representations is generally unknown) because the kernel of the canonical surjective group morphism onto $GL_n(\mathbb{Z}/p\mathbb{Z})$ is a $p$-group. $\endgroup$
    – Aurélien Djament
    Commented Sep 8, 2020 at 5:34
  • $\begingroup$ Ahh didn't know the problem was still open. Thanks for the replies. $\endgroup$
    – Niareh
    Commented Sep 9, 2020 at 15:24

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