论文标题
Coxeter组的Bruhat间隔的抛物线固定结构
The parabolic coset structure of Bruhat intervals in Coxeter groups
论文作者
论文摘要
在本文中，我们研究了抛物线亚组的coxeter组中Bruhat间隔的分解。我们的主要结果是，较低的Bruhat间隔与抛物线固定的交点包含独特的最大元素。作为应用程序，我们为Coxeter组元素的庞加莱多项式提供了一个分解公式。我们还表明，舒伯特品种的标准抛物线投影图的纤维本身就是舒伯特品种。
In this paper, we study the decomposition of Bruhat intervals in a Coxeter group with respect to cosets of a parabolic subgroup. Our main result is that the intersection of a lower Bruhat interval with a parabolic coset contains a unique maximal element. As an application, we give a decomposition formula for the Poincaré polynomial of a Coxeter group element. We also show that the fibers of standard parabolic projection maps on Schubert varieties are themselves Schubert varieties.
