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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

Online
ISSN
1435-4446
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Volume 14, Issue 5

Issues

A note on element centralizers in finite Coxeter groups

Matjaž Konvalinka / Götz Pfeiffer / Claas E. Röver
Published Online: 2011-08-29 | DOI: https://doi.org/10.1515/jgt.2010.074

Abstract

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 wW 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.

About the article

Received: 2010-05-07

Revised: 2010-09-20

Published Online: 2011-08-29

Published in Print: 2011-09-01


Citation Information: Journal of Group Theory, Volume 14, Issue 5, Pages 727–745, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2010.074.

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