On the modality of parabolic subgroups of linear algebraic groups
On the modality of parabolic subgroups of linear algebraic groups
复制标题
关于线性代数群的抛物线子群的模态
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
G. Röhrle
中科院分区：
文献类型：
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作者：
G. Röhrle
摘要：对于代数闭域k上的线性代数群G和G的抛物子群P，P的模态被定义为Lie Pu上的G-轨道族所依赖的参数的最大数目，它由mod P表示，其中Pu是P的幂单根。本说明的主要目的是将[19]中的两个基本“单调性”结果推广到正特征：（1）若G的半单自同构为θ，且P是Θ-稳定的，则mod PΘ≤ mod P.（2）若G是约化的，则chark是G的好素数，且H是G的一个极大环T <$P正规化的闭约化子群，则mod（P <$H）≤ mod P.
Abstract:For a linear algebraic group G over an algebraically closed field k and a parabolic subgroup P of G the modality of P is defined to be the maximal number of parameters upon which a family of G-orbits on Lie Pu depends and it is denoted by mod P, where Pu is the unipotent radical of P. The principal aim of this note is a generalization of two basic “monotonicity” results from [19] to positive characteristic: (1) If Θ is a semisimple automorphism of G and P is Θ-stable, then mod PΘ≤ mod P. (2) If G is reductive, char k is a good prime for G, and H is a closed reductive subgroup of G normalized by a maximal torus T⊂P of G, then mod (P∩H)≤ mod P.