Around Solomon’s Descent Algebras

  • C. Bonnafé
  • G. PfeifferEmail author


We study different problems related to the Solomon’s descent algebra Σ(W) of a finite Coxeter group (W,S): positive elements, morphisms between descent algebras, Loewy length... One of the main result is that, if W is irreducible and if the longest element is central, then the Loewy length of Σ(W) is equal to \(\displaystyle{\left\lceil\frac{|S|}{2}\right\rceil}\).


Solomon’s descent algebras Finite Coxeter group Loewy length 

Mathematics Subject Classifications (2000)

Primary 20F55 Secondary 05E99 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Labo. de Math. de Besançon (CNRS: UMR 6623)Université de Franche-ComtéBesançon CedexFrance
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland

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