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Involution products in Coxeter groups

Hart, Sarah B. and Rowley, P.J. (2011) Involution products in Coxeter groups. Journal of Group Theory 14 (2), pp. 251-259. ISSN 1435-4446.

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Official URL: http://dx.doi.org/10.1515/jgt.2010.053

Abstract

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero.

Item Type: Article
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Sarah Hart
Date Deposited: 19 Nov 2009 12:34
Last Modified: 17 Apr 2013 12:33
URI: http://eprints.bbk.ac.uk/id/eprint/811

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