FUNDAMENTAL REPRESENTATIONS OF Ga INTO 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 ${\mathbb{G}}_a⋊{\mathbb{G}}_m$ into $\text{SL}(3,k)$, and thereby we classify fundamental representations of ${\mathbb{G}}_a$ into $\text{SL}(3,k)$.