论文标题
SHI布置仅限于Weyl锥
Shi arrangements restricted to Weyl cones
论文作者
论文摘要
我们考虑了对Weyl锥的限制，它们与根本底片中的抗细胞的关系及其相交posets的限制。对于任何Weyl锥，我们提供区域之间的射箭，与锥体相交的平面和根本Poset的自然定义的子座的抗小构。这通过所有Weyl锥体的交叉点posets的Poincaré多项式提供了停车功能编号的细化。最后，我们将这些庞加莱的多项式解释为两个同构分级环的希尔伯特系列，一个是由varchenko-gel'fand ring产生的，另一个是我们称之为订单环，因为事实证明它与顺序多型阶段相关。
We consider the restrictions of Shi arrangements to Weyl cones, their relations to antichains in the root poset, and their intersection posets. For any Weyl cone, we provide bijections between regions, flats intersecting the cone, and antichains of a naturally-defined subposet of the root poset. This gives a refinement of the parking function numbers via the Poincaré polynomials of the intersection posets of all Weyl cones. Finally, we interpret these Poincaré polynomials as the Hilbert series of two isomorphic graded rings, one arising from the Varchenko-Gel'fand ring and another, which we call the order ring since it turns out to be naturally associated to the order polytope.
