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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 ...