TY - JOUR
T1 - On centralizers of parabolic subgroups in Coxeter groups
AU - Nuida, Koji
N1 - Funding Information:
A part of this work was supported by JSPS Research Fellowship (No. 16-10825).
PY - 2011/11
Y1 - 2011/11
N2 - Let W be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer ZW(WI) of an arbitrary parabolic subgroup WI into the center of WI, a Coxeter group and a subgroup defined by a 2-cell complex. Only information about finite parabolic subgroups is required in an explicit computation. By using our description of ZW(WI), we will be able to reveal a further strong property of the action of the third factor on the second factor, in particular on the finite irreducible components of the second factor.
AB - Let W be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer ZW(WI) of an arbitrary parabolic subgroup WI into the center of WI, a Coxeter group and a subgroup defined by a 2-cell complex. Only information about finite parabolic subgroups is required in an explicit computation. By using our description of ZW(WI), we will be able to reveal a further strong property of the action of the third factor on the second factor, in particular on the finite irreducible components of the second factor.
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U2 - 10.1515/JGT.2010.088
DO - 10.1515/JGT.2010.088
M3 - Article
AN - SCOPUS:80755126011
SN - 1433-5883
VL - 14
SP - 891
EP - 930
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 6
ER -