Homomorphisms from $\mathrm{SL}(2,k)$ to $\mathrm{SL}(4,k)$ in positive characteristic

Abstract

Let $k$ be an algebraically closed field of positive characteistic $p$ and let $\mathrm{SL}(n,k)$ denote the special linear algebraic group of degree $n$ over $k$. In this paper, we describe homomorphisms from $\mathrm{SL}(2,k)$ to $\mathrm{SL}(4,k)$. As by-products of this description, we give a classification of homomorphisms from $\mathrm{SL}(2,k)$ to $\mathrm{SL}(4,k)$ and describe the indecomposable decompositions of homomorphisms from $\mathrm{SL}(2,k)$ to $\mathrm{SL}(4,k)$.

105 pages