Overgroups of Levi subgroups I. The case of abelian unipotent radical

Abstract

In the present paper we prove sandwich classification for the overgroups of the subsystem subgroup $E(\Delta ,R)$ of the Chevalley group $G(\Phi ,R)$ for the three types of pair $(\Phi ,\Delta )$ (the root system and its subsystem) such that the group $G(\Delta ,R)$ is (up to torus) a Levi subgroup of the parabolic subgroup with abelian unipotent radical. Namely we show that for any such an overgroup $H$ there exists a unique pair of ideals $\sigma$ of the ring $R$ such that $E(\Phi ,\Delta ,R,\sigma )\le H\le N_{G(\Phi ,R)}(E(\Phi ,\Delta ,R,\sigma ))$.

37 pages, 3 figures

Cited by in corpus (2)

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