论文标题
复杂辫子组的抛物线亚组
Parabolic subgroups of complex braid groups
论文作者
论文摘要
在本文中，我们为与任意不可约合的复杂反射组相关的广义编织组引入了一类“抛物线”亚组，该组将其映射到反射组的抛物线亚组的集合中。除了在其他地方单独证明的一个情况外，我们证明该集合形成了一个晶格，因此抛物线亚组的交集是抛物线亚组。特别是，每个元素都接受抛物线封闭，这是包含它的最小抛物线亚组。我们此外，证明它提供了一种简单的复合体，该复合物概括了通常的编织组的曲线复合物。就实际反射组而言，该复合物概括了Cumplido，Gebhardt，González-Meneses和Wiest to to artin类型的Artin组提出的复合物。我们证明它具有相似的属性，并且同样猜测其双曲线。
In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group. Except for one case, which is proven separately elsewhere, we prove that this collection forms a lattice, so that intersections of parabolic subgroups are parabolic subgroups. In particular, every element admits a parabolic closure, which is the smallest parabolic subgroup containing it. We furthermore prove that it provides a simplicial complex which generalizes the curve complex of the usual braid group. In the case of real reflection groups, this complex generalizes the one previously introduced by Cumplido, Gebhardt, González-Meneses and Wiest for Artin groups of spherical type. We show that it shares similar properties, and similarly conjecture its hyperbolicity.
