BIROn - Birkbeck Institutional Research Online

# Commuting Involution Graphs in Classical Affine Weyl Groups

Hart, Sarah and Sbeiti Clarke, Amal (2018) Commuting Involution Graphs in Classical Affine Weyl Groups. Working Paper. Birkbeck, University of London, London, UK.

 Preview
Text
Preprint42hart.pdf - Author's Accepted Manuscript

## Abstract

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 $\C(\tilde W, X)$ 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 $\tilde D_n$.

Item Type: Monograph (Working Paper) Mathematical Sciences Preprint Series No.43 School of Business, Economics & Informatics > Economics, Mathematics and Statistics Sarah Hart 17 Sep 2018 12:52 16 Jun 2021 18:52 https://eprints.bbk.ac.uk/id/eprint/23909

## Statistics

Activity Overview
6 month trend