Zero excess and minimal length in finite coxeter groups

Hart, Sarah and Rowley, P.J. (2012) Zero excess and minimal length in finite coxeter groups. Journal of Group Theory 15 (4), pp. 497-512. ISSN 1435-4446.

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 $e(w) = 0 = E(w)$.

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• Zero excess and minimal length in finite coxeter groups. (deposited 10 Nov 2010 08:51)
  • Zero excess and minimal length in finite coxeter groups. (deposited 20 Dec 2012 11:39) [Currently Displayed]

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