论文标题
大型Artin组的抛物线亚组
Parabolic subgroups of large-type Artin groups
论文作者
论文摘要
我们表明，大型Artin组的适当抛物线亚组的Poset的几何实现具有收缩的几何形状。我们使用这种几何形状表明，在任意交叉点下，大型Artin组的抛物线亚组集是稳定的，并形成了包含的晶格。作为一种应用，我们表明，大型Artin组的抛物线亚组在根源下是稳定的，我们完全表征了词性稳定的抛物线亚组。 我们还使用这种几何视角来恢复和统一描述大型Artin组的抛物线亚组的正常符的结果。
We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of parabolic subgroups of a large-type Artin group is stable under arbitrary intersections and forms a lattice for the inclusion. As an application, we show that parabolic subgroups of large-type Artin groups are stable under taking roots and we completely characterise the parabolic subgroups that are conjugacy stable. We also use this geometric perspective to recover and unify results describing the normalisers of parabolic subgroups of large-type Artin groups.
