On the closures of orbits of fourth order matrix pencils

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Abstract

We state a simple criterion for nilpotency of an n × n matrix pencil with respect to the action of SLn(ℂ) × SL n(ℂ) × SL2(ℂ). We explicitly classify the orbits of matrix pencils for n = 4 and describe the hierarchy of closures of nilpotent orbits. We also prove that the algebra of invariants of the action of SLn(ℂ) × SLn(ℂ) × SL2 (ℂ) on ℂn ⊗ ℂn ⊗ ℂ2 is naturally isomorphic to the algebra of invariants of binary forms of degree n with respect to the action of SL2(ℂ).

Original languageEnglish
Pages (from-to)1047-1055
Number of pages9
JournalIzvestiya Mathematics
Volume66
Issue number5
DOIs
Publication statusPublished - Sep 2002
Externally publishedYes

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