Overgroups of Levi subgroups I. The case of abelian unipotent radical,St. Petersburg Mathematical Journal

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Overgroups of Levi subgroups I. The case of abelian unipotent radical
St. Petersburg Mathematical Journal ( IF 0.8 ) Pub Date : 2020-10-27 , DOI: 10.1090/spmj/1631
P. Gvozdevsky

Abstract:In the present paper, sandwich classification is established for the overgroups of the subsystem subgroup $E(\Delta ,R)$ of the Chevalley group $G(\Phi ,R)$ for the three types of the pair $(\Phi ,\Delta )$ (the root system and its subsystem) listed below such that the group $G(\Delta ,R)$ is (up to a torus) a Levi subgroup of the parabolic subgroup with Abelian unipotent radical. Namely, it is shown that for any overgroup

of this sort, there exists a unique pair of ideals $\sigma$ of the ring

with $E(\Phi ,\Delta ,R,\sigma )\le H\le N_{G(\Phi ,R)}(E(\Phi ,\Delta ,R,\sigma ))$ .

中文翻译：

Levi子群的超群I.阿贝尔单能根的情况

摘要：在本文中，针对Chevalley组的子系统子组的超群建立了三明治分类，用于下面列出的三种对对（根系统及其子系统），使得该组是（直到一个圆环）具有阿贝尔单能根的抛物线子群的一个Levi子群。即，示出的是对于任何overgroup这种，存在唯一的一对理想的环的带。 $E（\ Delta，R）$ $G（\ Phi，R）$ $（\ Phi，\ Delta）$ $G（\ Delta，R）$

$\ sigma$

$E（\ Phi，\ Delta，R，\ sigma）\ le H \ le N_ {G（\ Phi，R）}（E（\ Phi，\ Delta，R，\ sigma））$

更新日期：2020-10-30

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