Some four-dimensional orthogonal invariants

Shan Ren; Runxuan Zhang

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arXiv · 2504.10841

Some four-dimensional orthogonal invariants

Shan Ren·Runxuan Zhang

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Abstract

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.

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Shan Ren, Runxuan Zhang. 2025-04-15. Some four-dimensional orthogonal invariants. https://arxiv.org/abs/2504.10841

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