Götz Pfeiffer,
# Quiver Presentations for Descent Algebras of Exceptional Type.

25 pages.
Preprint IRL-GLWY-2008-002.
arXiv:0810.2743.

## Abstract.

The descent algebra of a finite Coxeter group $W$ is a basic
algebra, and as such it has a presentation as quiver with relations.
In recent work, we have developed a combinatorial framework which
allows us to systematically compute such a quiver presentation for a
Coxeter group of a given type. In this article, we use that
framework to determine quiver presentations for the descent algebras
of the Coxeter groups of exceptional or non-crystallographic type,
i.e., of type $E$_{6}, $E$_{7}, $E$_{8}, $F$_{4}, $H$_{3}, $H$_{4} or $I$_{2}(m).
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