The Loewy length of the descent algebra of type D

Details The Loewy length of the descent algebra of type D The Loewy length of the descent algebra of type D

2007-08-30

arxiv.org/abs/0708.4070v1

Mathematics

Representation Theory

10 pages

Scientific paper

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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