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

@article{Bishop2013OnTQ,
  title={On the quiver presentation of the descent algebra of the symmetric group},
  author={Marcus Bishop and G{\"o}tz Pfeiffer},
  journal={Journal of Algebra},
  year={2013},
  volume={383},
  pages={212-231}
}
View PDF on arXiv
3 Citations
Background Citations
2

Figures and Tables from this paper

3 Citations

Citation Type

Citation Type

On the Quiver Presentation of the Descent Algebra of the Hyperoctahedral Group
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of…
Diagonalization of Fix-Mahonian Matrices
Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of…
Topics in Hyperplane Arrangements

References

SHOWING 1-10 OF 18 REFERENCES
A QUIVER PRESENTATION FOR SOLOMON'S DESCENT ALGEBRA.
Quiver Presentations for Descent Algebras of Exceptional Type
The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as such it has a presentation as quiver with relations. In recent work, we have developed a combinatorial framework which…
On the quiver of the descent algebra
A decomposition of Solomon's descent algebra
A Decomposition of the Descent Algebra of a Finite Coxeter Group
The purpose of this paper is twofold. First we aim to unify previous work by the first two authors, A. Garsia, and C. Reutenauer (see [2], [3], [4], [5] and [10]) on the structure of the descent…
The Loewy Length of the Descent Algebra of Type D
In this article the Loewy length of the descent algebra of D2m + 1 is shown to be m + 2, for m ≥ 2, by providing an upper bound that agrees with the lower bound in Bonnafé and Pfeiffer (2006). The…
THE MODULE STRUCTURE OF SOLOMON'S DESCENT ALGEBRA
A close connection is uncovered between the lower central series of the free associative algebra of countable rank and the descending Loewy series of the direct sum of all Solomon descent algebras1n,…
A decomposition of the descent algebra of the hyperoctahedral group
Orthogonal idempotents in the descent algebra of Bn and applications
Solomon's Descent Algebra Revisited
Starting from a non-standard definition, the descent algebra of the symmetric group is investigated. Homomorphisms into the tensor product of smaller descent algebras are defined. They are used to…
...
1
2
...