论文标题
Weyl群上的原子长度
Atomic length on Weyl groups
论文作者
论文摘要
我们对称为原子长度的Weyl组定义了一个新的统计量，并研究了其组合和表示特性。在有限类型中，我们显示了原子长度的许多属性，这些属性让人想起通常长度的属性。此外，我们证明，除第二等级外，该统计量还描述了一个间隔。在仿射类型中，我们的结果阐明了经典的枚举问题，例如著名的格兰维尔 - 户外定理，关于核心分区的存在，通过将原子长度与晶体理论联系起来。
We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the properties of the usual length. Moreover, we prove that, with the exception of rank two, this statistic describes an interval. In affine types, our results shed some light on classical enumeration problems, such as the celebrated Granville-Ono theorem on the existence of core partitions, by relating the atomic length to the theory of crystals.
