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

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