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    Commuting Involution Graphs in classical affine Weyl Groups

    Hart, Sarah and Sbeiti Clarke, Amal (2020) Commuting Involution Graphs in classical affine Weyl Groups. Communications in Algebra 48 (7), pp. 2941-2957. ISSN 0092-7872.

    ComInvClassicalAffine Version 2 Comm in Alg.pdf - Author's Accepted Manuscript

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    In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$, with $\widetilde W$ its corresponding affine Weyl group. Our main result is that if $X$ is a conjugacy class of involutions in $\widetilde W$, then the commuting involution graph $\C(\widetilde W, X)$ is either disconnected or has diameter at most $n+2$. This bound is known to hold for types $\widetilde A_n$ and $\widetilde C_n$, so the main work of this paper is to prove the theorem for types $\widetilde B_n$ and $\widetilde D_n$.


    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 04 Feb 2020 09:37
    Last Modified: 24 Jan 2022 18:10


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