Innovations in Incidence Geometry
- Innov. Incidence Geom.
- Volume 12, Number 1 (2011), 111-140.
The twist conjecture for Coxeter groups without small triangle subgroups
We prove Mühlherr's twist conjecture for Coxeter systems $(W,S)$ which have no rank $3$ subsystems of type $2$-$3$-$n$ or $2$-$4$-$n$ ($n \geq 3$). In combination with known results this finishes the solution of the isomorphism problem for this class of groups. The condition on the diagram does not allow spherical rank $3$ subsystems, but our result covers “most” of the even Coxeter systems. With respect to earlier contributions, we develop a geometric technique to handle rank $2$ twists, in particular rotation twists which occur in the even case.
Innov. Incidence Geom., Volume 12, Number 1 (2011), 111-140.
Received: 19 August 2010
Accepted: 12 January 2011
First available in Project Euclid: 28 February 2019
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Weigel, Christian J. The twist conjecture for Coxeter groups without small triangle subgroups. Innov. Incidence Geom. 12 (2011), no. 1, 111--140. doi:10.2140/iig.2011.12.111. https://projecteuclid.org/euclid.iig/1551323071