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}
}

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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,… Expand

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… Expand