Tsukuba Journal of Mathematics

On finite factors of centralizers of parabolic subgroups in Coxeter groups

Koji Nuida

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It has been known that the centralizer ZW(WI) of a parabolic subgroup WI of a Coxeter group W is a split extension of a naturally defined reflection subgroup by a subgroup defined by a 2-cell complex $\mathscr{Y}$. In this paper, we study the structure of ZW(WI) further and show that, if I has no irreducible components of type An with 2 ≤ n < ∞, then every element of finite irreducible components of the inner factor is fixed by a natural action of the fundamental group of $\mathscr{Y}$. This property has an application to the isomorphism problem in Coxeter groups.

Article information

Tsukuba J. Math., Volume 36, Number 2 (2013), 235-294.

First available in Project Euclid: 21 January 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20E34: General structure theorems

Coxeter groups reflections parabolic subgroups centralizers finite factors


Nuida, Koji. On finite factors of centralizers of parabolic subgroups in Coxeter groups. Tsukuba J. Math. 36 (2013), no. 2, 235--294. doi:10.21099/tkbjm/1358777001. https://projecteuclid.org/euclid.tkbjm/1358777001

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