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 UNSPECIFIED, unpublished working paper. (Unpublished)

 Preview
Text
1261.pdf

## 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) Mathematics subject classification 20F55. A version of this will be submitted to a refereed journal. Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics Sarah Hart 10 Nov 2010 08:51 17 Apr 2013 12:33 http://eprints.bbk.ac.uk/id/eprint/1261