The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman

2008/03/05 by Riccardo Biagioli, Biagioli, Riccardo, Sara Faridi +3
Mathematics · #05E #13D #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05E #msc:13D

paper · pdf · doi:10.48550/arxiv.0803.0658

arxiv created 2008/03/05 · arxiv updated 2009/12/01

Abstract

Tanisaki introduced generating sets for the defining ideals of the schematic intersections of the closure of conjugacy classes of nilpotent matrices with the set of diagonal matrices. These ideals are naturally labeled by integer partitions. Given such a partition λ, we define several methods to produce a reduced generating set for the associated ideal I_λ. For particular shapes we find nice generating sets. By comparing our sets with some generating sets of I_λ arising from a work of Weyman, we find a counterexample to a related conjecture of Weyman.

Related

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