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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 UNSPECIFIED, unpublished working paper. (Unpublished)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 $e(w) = 0 = E(w)$.

Item Type: Monograph (Working Paper)
Additional Information: Mathematics subject classification 20F55. A version of this will be submitted to a refereed journal.
School or Research Centre: Birkbeck Schools and Research Centres > 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

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