The Representations of Automorphism Groups of $\mathfrak{o}$-modules of type $(\ell,1^n)$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909588693975040 |
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| author | Jackson, Alexander |
| author_facet | Jackson, Alexander |
| contents | 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 $q=|\mathfrak{o}_1|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Representations of Automorphism Groups of $\mathfrak{o}$-modules of type $(\ell,1^n)$ Jackson, Alexander Representation Theory 20G05 (Primary), 20C15 (Secondary) 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 $q=|\mathfrak{o}_1|$. |
| title | The Representations of Automorphism Groups of $\mathfrak{o}$-modules of type $(\ell,1^n)$ |
| topic | Representation Theory 20G05 (Primary), 20C15 (Secondary) |
| url | https://arxiv.org/abs/2501.18480 |