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arXiv · 2609.28195

Conjugation Differential Invariants of $\mathrm{SL}_2(\mathbb{F}_q)$ on trace-free matrices

Jonathan Elmer
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Abstract

Let $q=p^k$ be prime power, let $F= \mathbb{F}_q$ and let $V$ be the vector space of 2 by 2 matrices over $F$ with trace zero. Let $G = \mathrm{SL}_2(F)$. Then $G$ acts on $V$ via conjugation. Let $Ω= S(V^*) \otimes Λ(V^*)$ be the algebra of differential forms on $V$. A minimal generating set for $Ω^G$ when $q=3$ was computed by the author and Meyer. In this article we compute a minimal generating set for $Ω^G$ for all $q$.

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Jonathan Elmer. 2026-09-23. Conjugation Differential Invariants of $\mathrm{SL}_2(\mathbb{F}_q)$ on trace-free matrices. https://arxiv.org/abs/2609.28195

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