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A note on element centralizers in finite Coxeter groups
-
Matjaž Konvalinka
,
Götz Pfeiffer
Veröffentlicht/Copyright:
29. August 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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- Stabilizers of ℝ-trees with free isometric actions of FN
- On factorizations of finite groups with ℱ-hypercentral intersections of the factors
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Artikel in diesem Heft
- A proof that Thompson's groups have infinitely many relative ends
- Quadratic properties in group amalgams
- Stabilizers of ℝ-trees with free isometric actions of FN
- On factorizations of finite groups with ℱ-hypercentral intersections of the factors
- On the involution module of SL2(2ƒ)
- A note on element centralizers in finite Coxeter groups
- Lattice-defined classes of finite groups with modular Sylow subgroups
- On groups with all proper subgroups of finite exponent
- A case-free characterization of hyperbolic Coxeter systems
- Corrigendum: Some class size conditions implying solvability of finite groups
- On the q-tensor square of a group
