Angle-deformations in Coxeter groups

Marquis, Timothée; Mühlherr, Bernhard

doi:10.2140/agt.2008.8.2175

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Angle-deformations in Coxeter groups

Timothée Marquis and Bernhard Mühlherr

Algebraic & Geometric Topology 8 (2008) 2175–2208

DOI: 10.2140/agt.2008.8.2175

Abstract

The isomorphism problem for Coxeter groups has been reduced to its “reflection preserving version” by B Howlett and the second author. Thus, in order to solve it, it suffices to determine for a given Coxeter system $(W, R)$ all Coxeter generating sets $S$ of $W$ which are contained in $R^{W}$ , the set of reflections of $(W, R)$ . In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets $S \subseteq R^{W}$ which are sharp-angled with respect to $R$ .

Added 22 May 2012: The description of Figure 3 in Section 8.1 has been corrected.

Keywords

angle-deformation, Coxeter group, isomorphism problem, sharp-angled

Mathematical Subject Classification 2000

Primary: 20F55

Secondary: 51F15

References

Publication

Received: 21 February 2008

Revised: 19 October 2008

Accepted: 29 October 2008

Published: 3 December 2008

Corrected: 22 May 2012

Authors

Timothée Marquis
Université Libre de Bruxelles Département de Mathématiques Boulevard du Triomphe CP 216 Brussels, 1050 Belgium

Bernhard Mühlherr
Universität Giessen Mathematisches Institut Arndtstrasse 2 Giessen, D-35392 Germany

Volume 8, issue 4 (2008)