Representations of $\mathbb{G}_a \rtimes \mathbb{G}_m$ into ${\rm SL}(3, k)$ in positive characteristic

Abstract

Let $k$ be an algebraically closed field of positive characteristic $p$. In this article, we classify representations of $\mathbb{G}_a \rtimes \mathbb{G}_m$ into ${\rm SL}(3, k)$, and thereby we classify fundamental representations of $\mathbb{G}_a$ into ${\rm SL}(3, k)$.