On the root system of a coxeter group
On the root system of a coxeter group
复制标题
DOI：
10.1080/00927878208822738
复制
发表时间：
1982
影响因子：
0.7
通讯作者：
Vinay V. Deodhar
中科院分区：
文献类型：
--
作者：
Vinay V. Deodhar
众所周知，Weyl群的许多性质可以用相关的根系(有限的和积分的)来表述和证明。武断的科克塞特组合(W，S)的情况可能没有那么好理解。一个人知道(El，CH.V]，c61)可以与(W，S)具有类似于经典根系的性质的一组向量O相联系。我们称这个集合为(W，S)的(典范)根系。使用某种这样的向量集合来获得关于Coxeter基团的信息的想法隐含在C6,511中。本文利用0证明了Coxeter群的一些性质。
It is well-known that many properties of a Weyl group can be stated and proved in terms of the associated root system (finite and integral). The situation for an arbitrary Coxeter group (W, S) is perhaps not so well-understood. One knows (El, Ch. V], C61) that it is possible to associate to (W, S) a set of vectors O which has properties similar to a classical root-system. We call this set the (canonical) root system of (W, S). The idea of using some such set of vectors to obtain information about Coxeter groups is implicit in C6, 511. In the present article, we prove some more properties of Coxeter groups using 0.