On the maximum nilpotent orbit intersecting a centralizer in M(n,K)

2012/02/15 by Roberta Basili, Basili, Roberta
Mathematics · #14L30 #15A21 #15A27 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:14L30 #msc:15A21 #msc:15A27

paper · pdf · doi:10.48550/arxiv.1202.3369

arxiv created 2014/02/10 · arxiv updated 2014/02/11

Abstract

To any pair of commuting n x n nilpotent matrices it is associated a pair of partitions of n. We describe a maximal nilpotent subalgebra of the centralizer of a given nilpotent n x n matrix and prove a conjecture of Polona Oblak which consists in an algorithm for the determination of the maximum partition which forms with a given partition a pair with the previous property.

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