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 UNSPECIFIED, unpublished working paper. (Unpublished)
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Official URL: http://www.ems.bbk.ac.uk/research/wp
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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