Innovations in Incidence Geometry

The twist conjecture for Coxeter groups without small triangle subgroups

Christian J. Weigel

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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.

Article information

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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Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 51F15: Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]

Coxeter group twist conjecture


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.

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