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    Zero excess and minimal length in finite coxeter groups

    Hart, Sarah and Rowley, P.J. (2012) Zero excess and minimal length in finite coxeter groups. Journal of Group Theory 15 (4), pp. 497-512. ISSN 1435-4446.

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    Abstract

    Let \mathcal{W} be the set of strongly real elements of W, a Coxeter group. Then for $w \in \mathcal{W}$, $e(w)$, the excess of w, is defined by $e(w) = \min min \{l(x)+l(y) - l(w)| w = xy; x^2 = y^2 =1}$. When $W$ is finite we may also define E(w), the reflection excess of $w$. The main result established here is that if $W$ is finite and $X$ is a $W$-conjugacy class, then there exists $w \in X$ such that $w$ has minimal length in $X$ and $e(w) = 0 = E(w)$.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 20 Dec 2012 11:39
    Last Modified: 18 Jun 2021 10:01
    URI: https://eprints.bbk.ac.uk/id/eprint/5641

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