论文标题
Coxeter组的中间订单
The intermediate orders of a Coxeter group
论文作者
论文摘要
我们在与一组反射集相关的Coxeter组上定义了一类部分订单。在特殊情况下，这些位于左弱秩序和布鲁哈特秩序之间。我们证明这些posets是按长度函数进行分级的，并且正确的抛物线商上的投影始终保持订单。我们还介绍了$ k $ -bruhat图的概念，$ k $ -absolute长度和$ k $ -absolute订单，提出了一些相关的猜想和问题。
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that the projections on the right parabolic quotients are always order preserving. We also introduce the notion of $k$-Bruhat graph, $k$-absolute length and $k$-absolute order, proposing some related conjectures and problems.
