Author

Jonathan Elmer

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Preprint Sep 2026

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

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 $\Omega = S(V^*) \otimes \Lambda(V^*)$ be the algebra of differential forms on $V$. A minimal generating set for $\Omega^G$...

Jonathan Elmer · 0 citations

Preprint Jul 2026

Semi-Invariants of a Matrix and Covector

We prove the following theorem: let $\mathcal{M}_d$ denote the set of $d \times d$ matrices over an infinite field $K$, and let ${(K^d)^*}$ be the set of row vectors. Define an action of $\mathrm{SL}_d(K)$ on $X:= \mathcal{M}_d \oplus (K^d)^*$ by \[ g \cdot (A,\phi) = (gAg^{-1}, \phi g^{-1}).\] Then $K[X]^{\mathrm{SL}_...

Jonathan Elmer · 0 citations