Homomorphisms between Chevalley groups of types \(C_ n\) and \(G_ 2\) over finite fields (Q1362870)

Let \(\Sigma\) be an indecomposable root system and \(L\) a lattice between the weight lattice and root lattice of \(\Sigma\). Denote by \(G(\Sigma,F,L)\) the Chevalley group associated with \(\Sigma\) and \(L\) over a field \(F\). The author determines all nontrivial homomorphisms from \(G(\Sigma,k,L_1)\) to \(G(\Sigma,K,L_2)\), where \(\Sigma\) is of type \(C_n\) or \(G_2\), \(k\) and \(K\) are finite fields of characteristic \(p\) with \(p\neq 2\) in the case of type \(C_n\) and \(p\neq 2,3\) in the case of type \(G_2\).