Finding the Quiver of the Descent Algebras

   Franco Saliola (UQAM)

Abstract: This will be a survey outlining the current status of my project to study of the representation theory of the descent algebra of a finite Coxeter group. It will concentrate on the descent algebra of the symmetric group because the current results are better in this case. The approach utilizes what I call the "geometric approach" to the descent algebra: there is a semigroup algebra constructed from the reflection arrangement of the Coxeter group that contains the descent algebra. The quiver of this semigroup algebra will be constructed and it will be used to get information about the quiver of the descent algebra.

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