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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 5, Pages 183–192 (Mi izv405)  

This article is cited in 2 scientific papers (total in 2 papers)

On the closures of orbits of fourth order matrix pencils

D. D. Pervouchine


Abstract: We state a simple criterion for nilpotency of an $n\times n$ matrix pencil with respect to the action of $\operatorname{SL}_n(\mathbb C)\times \operatorname{SL}_n(\mathbb C) \times\operatorname{SL}_2(\mathbb C)$. 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 $\operatorname{SL}_n(\mathbb C)\times \operatorname{SL}_n(\mathbb C)\times\operatorname{SL}_2(\mathbb C)$ on $\mathbb C_n\otimes\mathbb C_n\otimes\mathbb C_2$ is naturally isomorphic to the algebra of invariants of binary forms of degree $n$ with respect to the action of $\operatorname{SL}_2(\mathbb C)$.

DOI: https://doi.org/10.4213/im405

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English version:
Izvestiya: Mathematics, 2002, 66:5, 1047–1055

Bibliographic databases:

UDC: 512.643+512.813+512.815
MSC: 14L30, 15A72, 20G05
Received: 27.03.2001
Revised: 08.05.2002

Citation: D. D. Pervouchine, “On the closures of orbits of fourth order matrix pencils”, Izv. RAN. Ser. Mat., 66:5 (2002), 183–192; Izv. Math., 66:5 (2002), 1047–1055

Citation in format AMSBIB
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\by D.~D.~Pervouchine
\paper On the closures of orbits of fourth order matrix pencils
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 5
\pages 183--192
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1965939}
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\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 5
\pages 1047--1055
\crossref{https://doi.org/10.1070/IM2002v066n05ABEH000405}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-4544240544}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. de Graaf W.A. Vinberg E.B. Yakimova O.S., “An Effective Method to Compute Closure Ordering for Nilpotent Orbits of Theta-Representations”, J. Algebra, 371 (2012), 38–62  crossref  mathscinet  zmath  isi  scopus
    2. Panyushev D.I., Yakimova O.S., “Semi-Direct Products of Lie Algebras and Covariants”, J. Algebra, 490 (2017), 283–315  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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