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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 ...

#### Cohomology of Coxeter arrangements and Solomon's descent algebra

(American Mathematical Society, 2014-06-19)

We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ...

#### 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 reflection subgroups of finite Coxeter groups

(Taylor & Francis, 2013-06-14)

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its ...