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arXiv · 0708.4070

The Loewy length of the descent algebra of type D

Franco V. Saliola
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Abstract

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.

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Franco V. Saliola. 2007-08-30. The Loewy length of the descent algebra of type D. https://arxiv.org/abs/0708.4070

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