Overgroups of subsystem subgroups in exceptional groups: 2A1-proof

In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\mathrm{\Delta },R)$ of the Chevalley group $G(\mathrm{\Phi },R)$ where $\mathrm{\Phi }$ is a simply laced root sysetem and $\mathrm{\Delta }$ is its sufficiently large subsystem. Namely we show that for any such an overgroup $H$ there exists a unique net of ideals $\sigma$ of the ring $R$ such that $E(\Phi,\Delta,R,\sigma)\le H\le {\mathop{$\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{b}$}\nolimits}_{G(\Phi,R)}(L(\sigma))$where$E(\Phi,\Delta,R,\sigma)$isanelementarysubgroupassociatedwiththenetand$L(\sigma)$ is a corresponding subalgebra of the Chevalley Lie algebra.