%0 Journal Article
%T The Loewy length of the descent algebra of type D
%A Franco V. Saliola
%J Mathematics
%D 2007
%I arXiv
%X The Loewy length of the descent algebra of type D_{2m+1} is shown to be m+2, for m \geq 2, by providing an upper bound that agrees with the lower bound in \cite{BonnafePfeiffer2006}. The bound is obtained by showing that the length of the longest path in the quiver of the descent algebra of D_{2m+1} is at most m+1. To achieve this bound, the geometric approach to the descent algebra is used, in which the descent algebra of a finite Coxeter group is identified with an algebra associated to the reflection arrangement of the group.
%U http://arxiv.org/abs/0708.4070v1