Peer-Reviewed Journal Details
Mandatory Fields
Authors
Konvalinka, M,Pfeiffer, G,Rover, CE
Year
2011
Month
September
Journal
Journal Of Group Theory
Title
A note on element centralizers in finite Coxeter groups
Status
Published
Times Cited
()
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Search Keyword
PARABOLIC SUBGROUPS NORMALIZERS INVOLUTIONS
Volume
14
Issue
Start Page
727
End Page
745
Abstract
The normalizer N-W(W-J) of a standard parabolic subgroup W-J of a finite Coxeter group W splits over the parabolic subgroup with complement N-J consisting of certain minimal length coset representatives of W-J 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 D-n) the centralizer C-W(w) of an element w epsilon W is in a similar way a semidirect product of the centralizer of w in a suitable small parabolic subgroup W-J with complement isomorphic to the normalizer complement N-J. 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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DOI Link
DOI 10.1515/JGT.2010.074
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