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arXiv · 2501.18480

The Representations of Automorphism Groups of $\mathfrak{o}$-modules of type $(\ell,1^n)$

Alexander Jackson
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Abstract

Let $\mathfrak{o}$ be the valuation ring of a non-Archimedean local field with finite residue field. We give a procedure to find the representation zeta polynomial of $\mathrm{Aut}_\mathfrak{o}(\mathfrak{o}_\ell\oplus\mathfrak{o}_1^{\oplus n})$ by induction on $n$. In particular, we show that the dimensions of the representations are given by evaluating finitely many polynomials at $q=|\mathfrak{o}_1|$.

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BibTeXRIS

Alexander Jackson. 2025-01-30. The Representations of Automorphism Groups of $\mathfrak{o}$-modules of type $(\ell,1^n)$. https://arxiv.org/abs/2501.18480

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