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
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
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