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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 , ISSN 0092-7872. (In Press)

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    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 $\widetilde W$ 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 $\widetilde D_n$.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 04 Feb 2020 09:37
    Last Modified: 20 Jul 2020 23:57
    URI: http://eprints.bbk.ac.uk/id/eprint/30779

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