Matrix generators for Weil representations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913114782433280 |
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| author | Korhonen, Mikko |
| author_facet | Korhonen, Mikko |
| contents | Let $r$ be an odd prime and $\mathbb{F}$ a field containing a primitive $r$th root of unity. Then for all $\ell \geq 1$, there is a faithful representation $f: \operatorname{Sp}_{2\ell}(r) \rightarrow \operatorname{GL}_{r^\ell}(\mathbb{F})$ called the Weil representation. We provide explicit matrices generating $\operatorname{Sp}_{2\ell}(r)$ in $\operatorname{GL}_{r^\ell}(\mathbb{F})$, which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of $\operatorname{Sp}_{2\ell}(r)$, which are of degree $(r^{\ell} \pm 1)/2$ and arise as irreducible constituents of the Weil representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix generators for Weil representations Korhonen, Mikko Group Theory Representation Theory 20H20, 20C99 Let $r$ be an odd prime and $\mathbb{F}$ a field containing a primitive $r$th root of unity. Then for all $\ell \geq 1$, there is a faithful representation $f: \operatorname{Sp}_{2\ell}(r) \rightarrow \operatorname{GL}_{r^\ell}(\mathbb{F})$ called the Weil representation. We provide explicit matrices generating $\operatorname{Sp}_{2\ell}(r)$ in $\operatorname{GL}_{r^\ell}(\mathbb{F})$, which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of $\operatorname{Sp}_{2\ell}(r)$, which are of degree $(r^{\ell} \pm 1)/2$ and arise as irreducible constituents of the Weil representations. |
| title | Matrix generators for Weil representations |
| topic | Group Theory Representation Theory 20H20, 20C99 |
| url | https://arxiv.org/abs/2510.12261 |