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

Abstract

In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\Delta ,R)$ of the Chevalley group $G(\Phi ,R)$ where $\Phi$ is a simply laced root sysetem and $\Delta$ 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 $E(\Phi ,\Delta ,R,\sigma )\le H\le {\mathrm{Stab}}_{G(\Phi ,R)}(L(\sigma ))$ where $E(\Phi ,\Delta ,R,\sigma )$ is an elementary subgroup associated with the net and $L(\sigma )$ is a corresponding subalgebra of the Chevalley Lie algebra.

25 pages, to appear in St.Petersburg Math Journal

References in corpus (2)

• Structure of Chevalley groups over rings via universal localization
• Overgroups of Levi subgroups I. The case of abelian unipotent radical

Cited by in corpus (1)

• Overgroups of subsystem subgroups in exceptional groups: nonideal levels