例外群中子系统子群的过群:2a1证明

P. Gvozdevsky
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引用次数: 2

摘要

本文证明了Chevalley群$G(\Phi,R)$的子系统子群$E(\Delta,R)$的过群的一个弱形式的夹心分类,其中$\Phi$是一个单带根系统,$\Delta$是它的足够大子系统。也就是说,我们证明了对于任何这样的过群$H$,存在一个环$R$的唯一理想网$\sigma$,使得$E(\Phi,\Delta,R,\sigma)\le H\le {\mathop{\mathrm{Stab}}\nolimits}_{G(\Phi,R)}(L(\sigma))$,其中$E(\Phi,\Delta,R,\sigma)$是与网相关联的初等子群,$L(\sigma)$是Chevalley Lie代数的相应子代数。
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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 $E(\Delta,R)$ of the Chevalley group $G(\Phi,R)$ where $\Phi$ is a symply 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 $E(\Phi,\Delta,R,\sigma)\le H\le {\mathop{\mathrm{Stab}}\nolimits}_{G(\Phi,R)}(L(\sigma))$ 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.
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