论文标题
经典和仿射组的弱顺序的特征多项式
Characteristic polynomials of the weak order on classical and affine Coxeter groups
论文作者
论文摘要
我们找到了一个简单的产品公式，用于在弱顺序下具有固定下降集的置换的特征多项式。作为推论，我们获得了一个简单的产品公式，用于交替排列的特征多项式。我们将这些结果推广到Coxeter组。我们还找到了用于经典Coxeter组的特征多项式生成函数的公式，该公式与仿射Coxeter基团有关。
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating permutations. We generalize these results to Coxeter groups. We also find a formula for the generating function for the characteristic polynomials of classical Coxeter groups, which is then related to affine Coxeter groups.
