Tsukuba Journal of Mathematics

On finite factors of centralizers of parabolic subgroups in Coxeter groups

Koji Nuida

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Abstract

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

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

Dates
First available in Project Euclid: 21 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1358777001

Digital Object Identifier
doi:10.21099/tkbjm/1358777001

Mathematical Reviews number (MathSciNet)
MR3058241

Zentralblatt MATH identifier
1276.20045

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

Keywords
Coxeter groups reflections parabolic subgroups centralizers finite factors

Citation

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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