Journal of Group Theory
Editor-in-Chief: Parker, Christopher W.
Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus
6 Issues per year
IMPACT FACTOR 2017: 0.581
CiteScore 2017: 0.53
SCImago Journal Rank (SJR) 2017: 0.778
Source Normalized Impact per Paper (SNIP) 2017: 0.893
Mathematical Citation Quotient (MCQ) 2017: 0.45
A note on element centralizers in finite Coxeter groups
The normalizer NW (WJ ) of a standard parabolic subgroup WJ of a finite Coxeter group W splits over the parabolic subgroup with complement NJ consisting of certain minimal length coset representatives of WJ in W. In this note we show that (with the exception of a small number of cases arising from a situation in Coxeter groups of type Dn ) the centralizer CW (w) of an element w ∈ W is in a similar way a semidirect product of the centralizer of w in a suitable small parabolic subgroup WJ with complement isomorphic to the normalizer complement NJ . Then we use this result to give a new short proof of Solomon's Character Formula and discuss its connection to MacMahon's master theorem.
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