Some four-dimensional orthogonal invariants
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913794848980992 |
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| author | Ren, Shan Zhang, Runxuan |
| author_facet | Ren, Shan Zhang, Runxuan |
| contents | Let $p$ be an odd prime and $\mathbb{F}_p$ be the prime field of order $p$. Consider a $2$-dimensional orthogonal group $G$ over $\mathbb{F}_p$ acting on the standard representation $V$ and the dual space $V^*$. We compute the invariant ring $\mathbb{F}_p[V\oplus V^*]^G$ via explicitly exhibiting a minimal generating set. Our method finds an application of $s$-invariants appeared in covariant theory of finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some four-dimensional orthogonal invariants Ren, Shan Zhang, Runxuan Commutative Algebra 13A50 Let $p$ be an odd prime and $\mathbb{F}_p$ be the prime field of order $p$. Consider a $2$-dimensional orthogonal group $G$ over $\mathbb{F}_p$ acting on the standard representation $V$ and the dual space $V^*$. We compute the invariant ring $\mathbb{F}_p[V\oplus V^*]^G$ via explicitly exhibiting a minimal generating set. Our method finds an application of $s$-invariants appeared in covariant theory of finite groups. |
| title | Some four-dimensional orthogonal invariants |
| topic | Commutative Algebra 13A50 |
| url | https://arxiv.org/abs/2504.10841 |