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December 2012 On finite factors of centralizers of parabolic subgroups in Coxeter groups
Koji Nuida
Tsukuba J. Math. 36(2): 235-294 (December 2012). DOI: 10.21099/tkbjm/1358777001

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.

Citation

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Koji Nuida. "On finite factors of centralizers of parabolic subgroups in Coxeter groups." Tsukuba J. Math. 36 (2) 235 - 294, December 2012. https://doi.org/10.21099/tkbjm/1358777001

Information

Published: December 2012
First available in Project Euclid: 21 January 2013

zbMATH: 1276.20045
MathSciNet: MR3058241
Digital Object Identifier: 10.21099/tkbjm/1358777001

Subjects:
Primary: 20F55
Secondary: 20E34

Rights: Copyright © 2013 University of Tsukuba, Institute of Mathematics

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Vol.36 • No. 2 • December 2012
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