On pairs of commuting nilpotent matrices

DOI10.1007/s00031-008-9045-6zbMath1168.15009arXiv0712.2813OpenAlexW2150521838MaRDI QIDQ1024629

Polona Oblak, Tomasž Košir

Publication date: 17 June 2009

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2813

zbMATH Keywords

Jordan canonical formHilbert functionGorenstein algebranilpotent matrixMacaulay's theoremidempotent mapnilpotent commutator

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Algebraic systems of matrices (15A30) Canonical forms, reductions, classification (15A21)

Related Items (8)

On the maximal nilpotent orbit that intersects the centralizer of a matrix ⋮ On the nilpotent commutator of a nilpotent matrix ⋮ Commuting nilpotent matrices and Artinian algebras. ⋮ Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix ⋮ The poset of the nilpotent commutator of a nilpotent matrix ⋮ The smallest part of the generic partition of the nilpotent commutator of a nilpotent matrix ⋮ Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit ⋮ Artinian algebras and Jordan type

Cites Work

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• Pairs of commuting nilpotent matrices, and Hilbert function
• Two-generated commutative subalgebras of \(M_ n(F)\)
• On the irreducibility of commuting varieties of nilpotent matrices
• Nilpotent commuting varieties of reductive Lie algebras
• Principal nilpotent pairs in a semisimple Lie algebra. I
• Two results on centralisers of nilpotent elements
• Jordan forms for mutually annihilating nilpotent pairs
• The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
• Punctual Hilbert schemes
• Associated graded algebra of a Gorenstein Artin algebra
• Lie Group Representations on Polynomial Rings
• Symmetric pairs and associated commuting varieties
• Nilpotent pairs, dual pairs, and sheets
• The variety of pairs of commuting nilpotent matrices is irreducible

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