BIROn - Birkbeck Institutional Research Online

    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 UNSPECIFIED, unpublished working paper. (Unpublished)

    WarningThere is a more recent version of this item available.
    [img]
    Preview
    Text
    1261.pdf

    Download (194kB) | Preview

    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 Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 10 Nov 2010 08:51
    Last Modified: 17 Apr 2013 12:33
    URI: http://eprints.bbk.ac.uk/id/eprint/1261

    Available Versions of this Item

    Statistics

    Downloads
    Activity Overview
    93Downloads
    94Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item