A Quiver Presentation for Solomon's Descent Algebra.
The descent algebra is a subalgebra of the group algebra
of a finite Coxeter group , which supports a homomorphism with nilpotent
kernel and commutative image in the character ring of . Thus
is a basic algebra, and as such it has a presentation as a
quiver with relations. Here we construct as a quotient of a
subalgebra of the path algebra of the Hasse diagram of the Boolean lattice
of all subsets of , the set of simple reflections in . From this
construction we obtain some general information about the quiver of
and an algorithm for the construction of a quiver presentation
for the descent algebra of any given finite Coxeter group .
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