经典仿射外尔群的交换对合图
Commuting Involution Graphs in Classical Affine Weyl Groups
摘要：
本文研究了经典仿射外尔群中的交换对合图。设$W$是秩为$n$的经典Weyl群，$\tilde W$是其对应的仿射Weyl群.我们的主要结果是：如果$X$是$\tilde W$中对合的共轭类，则交换对合图$\mathcal{C}(\tilde W, X)$是不连通的或直径至多为$n+2$ .已知这个界对于$\tilde A_n$和$\tilde C_n$型是成立的，所以本文的主要工作是证明$\tilde B_n$和$\tilde D_n$型的定理.
英文摘要：
In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$, with $\tilde W$ its corresponding affine Weyl group. Our main result is that if $X$ is a conjugacy class of involutions in $\tilde W$, then the commuting involution graph $\mathcal{C}(\tilde W, X)$ is either disconnected or has diameter at most $n+2$. This bound is known to hold for types $\tilde A_n$ and $\tilde C_n$, so the main work of this paper is to prove the theorem for types $\tilde B_n$ and $\tilde D_n$.
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