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Commuting Involution Graphs in Classical Affine Weyl Groups by Hart, Sarah; Clarke, Amal Sbeiti is a scholarly article available to read on EtoBox.

What is Commuting Involution Graphs in Classical Affine Weyl Groups about?

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 $\tilde D_n$.

Author

Hart, Sarah; Clarke, Amal Sbeiti

Published

2018

Language

EN