论文标题
叶绿体中壁co的方向
Orientation of alcoves in affine Weyl groups
论文作者
论文摘要
令$ w $为不可约的Weyl群，其Aggine Weyl Group。在先前的工作中，作者引入了一个仿射品种$ \ wideHat {x} _ {w_a} $，称为$ w_a $的shi品种，其整体积分与$ w_a $进行了两者的培训。 $ \ wideHat {x} _ {w_a} $的不可约组件的集合在组理论，组合和几何形状的相交中提供了结果。在本文中，我们以第一组的$ w $和shi品种的不可约组件来表达壁co的方向的概念。我们还提供模块化方程，以SHI系数有效地描述具有相同方向的特性。
Let $W$ be an irreducible Weyl group and $W_a$ its affine Weyl group. In a previous work the author introduced an affine variety $\widehat{X}_{W_a}$, called the Shi variety of $W_a$, whose integral points are in bijection with $W_a$. The set of irreducible components of $\widehat{X}_{W_a}$ provided results at the intersection of group theory, combinatorics and geometry. In this article we express the notion of orientation of alcoves in terms of the first group of cohomogoly of $W$ and in terms of the irreducible components of the Shi variety. We also provide modular equations in terms of Shi coefficients that describe efficiently the property of having the same orientation.
