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#### Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight

(Elsevier, 2014-11-06)

In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the p-th graded ...

#### Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six

(Elsevier, 2013-01-08)

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from ...

#### An inductive approach to Coxeter arrangements and Solomon's descent algebra

(Springer Verlag, 2012-07-20)

In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional ...

#### Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four

(Elsevier, 2012-06-03)

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced ...

#### On the quiver presentation of the descent algebra of the symmetric group

(Elsevier, 2013-03-18)

We describe a presentation of the descent algebra of the symmetric group G(n) as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic image of an algebra of ...