论文标题
与卡特图关联的根部集之间的过渡
Transitions between root subsets associated with Carter diagrams
论文作者
论文摘要
对于与具有相同$ ade $类型和相同大小的两个卡特图关联的任何两个根子集，我们构造了一个将一个子集映射到另一个子集的过渡矩阵。这两个子集之间的过渡是以某种规范的方式进行的，从而完全影响一个根，以便将此根映射到某些根子系统中的最小元素。构造的过渡是交往。结果表明，在Weyl组的作用下，与给定的Carter图相关的所有根部都有偶联。在增强的dynkin图$δ（e_6）$，$δ（e_7）$和$δ（e_8）$（由dynkinkinkin-Minchenko引入）和卡特图之间观察到数值关系。这种关系呼应了林金（Ringel），罗森菲尔德（Rosenfeld）和贝兹（Baez）获得的$ 2-4-8 $的断言，在完全不同的情况下，关于dynkin图$ e_6 $，$ e_7 $，$ e_8 $。
For any two root subsets associated with two Carter diagrams that have the same $ADE$ type and the same size, we construct the transition matrix that maps one subset to the other. The transition between these two subsets is carried out in some canonical way affecting exactly one root, so that this root is mapped to the minimal element in some root subsystem. The constructed transitions are involutions. It is shown that all root subsets associated with the given Carter diagram are conjugate under the action of the Weyl group. A numerical relationship is observed between enhanced Dynkin diagrams $Δ(E_6)$, $Δ(E_7)$ and $Δ(E_8)$ (introduced by Dynkin-Minchenko) and Carter diagrams. This relationship echoes the $2-4-8$ assertions obtained by Ringel, Rosenfeld and Baez in completely different contexts regarding the Dynkin diagrams $E_6$, $E_7$, $E_8$.
