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    Zero excess and minimal length in finite coxeter groups

    Hart, Sarah B. and Rowley, P.J. (2010) Zero excess and minimal length in finite coxeter groups. Working Paper. UNSPECIFIED, unpublished working paper. (Unpublished)

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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: Monograph (Working Paper)
    Additional Information: Mathematics subject classification 20F55. A version of this will be submitted to a refereed journal.
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hart
    Date Deposited: 10 Nov 2010 08:51
    Last Modified: 09 Aug 2023 12:29
    URI: https://eprints.bbk.ac.uk/id/eprint/1261

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