Search
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.