On the number of conjugacy classes in finite groups of lie type
On the number of conjugacy classes in finite groups of lie type
复制标题
关于有限李型群中的共轭类数
DOI：
10.1080/00927878508823204
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发表时间：
1985
影响因子：
0.7
通讯作者：
D. Deriziotis
中科院分区：
文献类型：
--
作者：
D. Deriziotis
0型，它们包括有限Chevalley群，Steinberg-Tits群，Suzuki群和Ree群. J. Humphreys在[11 j]中，在Chevalley群Go的p-模表示理论的背景下，引入了一个称为Go的Brauer复形的几何对象（另见他最近的工作1121）。在前一篇文章（71）中，我们定义了这种复形的适当形式，并研究了它的一些性质，由此得到Chevalley群Go中半单元素共轭类的3个几何参数化。本文将Erauer复形的定义推广到任何有限Lie型群G，从而证明了文[171]中定理3.3在一般情况下成立。这是在52。在53中，我们证明了Ga中半单元素的共轭类的数目，这些共轭类具有它们的
0 type and they include the finite Chevalley groups, the Steinberg-Tits groups, the Suzuki groups and the Ree groups. J. Humphreys in [llj introduced, in the context of the p-modular representation theory of a Chevalley group Go, a geometrical object called the Brauer complex of Go (see also his more recent work 1121). In a previous paper (71 we defined this complex in a suitable form and studied some of its properties from which w~ obtained 3 geometrical parametrization of the conjugacy classes of semisimple elements in a Chevalley group Go. In the present paper our definition of the Erauer complex is extended to any finite group G of Lie type and o we prove that Theorem 3.3 in 171 holds in the general case. This is done in 52. I n 53, we show that the number of conjugacy classes of semisimple elements in Ga, which have the property that their