Elliptic centralizers in Weyl groups and their coinvariant representations
Elliptic centralizers in Weyl groups and their coinvariant representations
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Weyl 群中的椭圆中心化器及其协变表示
DOI：
10.1090/s1088-4165-2011-00377-0
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Mark Reeder
中科院分区：
文献类型：
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作者：
Mark Reeder
Weyl群中椭圆元w的中心化子C（w）在根格中的w-共不变量群上具有自然辛表示.我们给出了这种表示的基本性质，沿着应用于p-adic群分类极大环面和计算L包中的诱导数据以及阐明中心化器C（w）本身的结构.我们给出了W（E8）中每个椭圆中心化子的共不变表示的结构，并改进了Springer椭圆正则元的理论，给出了生成C（w）的显式复反射。的情况下，w有秩序的三个详细审查，连接到数学的世纪。该方法的一个变体恢复子群W（H4）W（E8）。
The centralizer C(w) of an elliptic element w in a Weyl group has a natural symplectic representation on the group ofw-coinvariants in the root lattice. We give the basic properties of this representation, along with applications to p-adic groups classifying maximal tori and computing inducing data in Lpackets as well as to elucidating the structure of the centralizer C(w) itself. We give the structure of each elliptic centralizer in W (E8) in terms of its coinvariant representation, and we refine Springer’s theory for elliptic regular elements to give explicit complex reflections generating C(w). The case where w has order three is examined in detail, with connections to mathematics of the 19th century. A variation of the methods recovers the subgroup W (H4) ⊂ W (E8).