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A note on element centralizers in finite Coxeter groups
-
Matjaž Konvalinka
,
Götz Pfeiffer
Published/Copyright:
August 29, 2011
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 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.
Received: 2010-05-07
Revised: 2010-09-20
Published Online: 2011-08-29
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
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