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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