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Now showing items 1-10 of 12

#### 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 ...

#### 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 ...

#### The BMR freeness conjecture for the 2-reflection groups

(American Mathematical Society, 2016-10-12)

We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections.

#### 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 ...

#### 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 ...

#### Computing the table of marks of a cyclic extension

(American Mathematical Society, 2012-02-24)

The subgroup pattern of a finite group C is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the ...

#### An algorithm for the unit group of the Burnside ring of a finite group

(Cambridge University Press, 2007-01)

In this note we present an algorithm for the construction of the unit group of
the Burnside ring Ω(G) of a finite group G from a list of representatives of the
conjugacy classes of subgroups of G.