论文标题
shi品种对应于息叶基团
Shi variety corresponding to an affine Weyl group
论文作者
论文摘要
令$ w $为不可约的Weyl群，其Aggine Weyl Group。在本文中，我们表明存在$ w_a $与仿射品种的积分点之间的两次射击，表示为$ \ widehat {x} _ {w_a} $，我们称之为$ w_a $的shi品种。为了这样做，我们使用了仿生中的Jian-Yi Shi对壁co的表征。然后，我们进一步研究了这个品种。我们突出显示了$ \ wideHat {x} _ {w_a} $的不可约组件的组合属性，我们展示了它们与基本并行派制的$ p _ {\ nathcal {h h}} $之间的关系。
Let $W$ be an irreducible Weyl group and $W_a$ its affine Weyl group. In this article we show that there exists a bijection between $W_a$ and the integral points of an affine variety, denoted $\widehat{X}_{W_a}$, which we call the Shi variety of $W_a$. In order to do so, we use Jian-Yi Shi's characterization of alcoves in affine Weyl groups. We then study this variety further. We highlight combinatorial properties of the irreducible components of $\widehat{X}_{W_a}$ and we show how they are related to a fundamental parallelepiped $P_{\mathcal{H}}$.
