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# Maximal length elements of excess zero in finite Coxeter Groups

Hart, Sarah and Rowley, P. (2018) Maximal length elements of excess zero in finite Coxeter Groups. Journal of Group Theory 21 (5), ISSN 1435-4446.

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21274.pdf - Author's Accepted Manuscript

## Abstract

Here we prove that for W a finite Coxeter group and C a conjugacy class of W, there is always an element of C of maximal length in C which has excess zero. An element w \in W has excess zero if there exist elements $\sigma, \tau \in W$ such that $\sigma^2 = \tau^2 = 1, w = \sigma\tau$ and \ell(w) = \ell(\sigma) + \ell(\tau), with \ell being the length function on W.

Item Type: Article This is the submitted version that has been accepted (14 Feb 2018); it was accepted subject to some minor changes suggested by the referees which we will be making, so this version is not the final version that will be published. School of Business, Economics & Informatics > Economics, Mathematics and Statistics Sarah Hart 04 Jun 2018 12:43 12 Feb 2021 21:33 https://eprints.bbk.ac.uk/id/eprint/21274