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The Loewy length of the descent algebra of type D

2007/08/30 by Franco Saliola, Franco V. Saliola, Saliola, Franco V. · 1 citation
Mathematics · #05E99 (Primary) #20F55 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E99 #msc:20F55

paper · pdf · doi:10.48550/arxiv.0708.4070

10 pages

arxiv created 2007/08/30 · openalex publication_date 2007/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Loewy length of the descent algebra of type D2m+1 is shown to be m+2, for m ≥ 2, by providing an upper bound that agrees with the lower bound in \citeBonnafePfeiffer2006. The bound is obtained by showing that the length of the longest path in the quiver of the descent algebra of D2m+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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