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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 5, Pages 133–146 (Mi izv306)  

This article is cited in 5 scientific papers (total in 5 papers)

Invariants and orbits of the standard $(\mathrm SL_4(\mathbb C)\times\mathrm SL_4(\mathbb C)\times\mathrm SL_2(\mathbb C))$-module

D. D. Pervouchine


Abstract: We consider the natural linear representation of the group $\mathrm SL_4(\mathbb C)\times\mathrm SL_4(\mathbb C)\times\mathrm SL_2(\mathbb C)$ on the space $\mathbb C^4\otimes\mathbb C^4\otimes\mathbb C^2$. Using the embedding of this representation in the adjoint representation of the Lie algebra $E_7$, we classify the orbits and find the generators of the algebra of invariants.

DOI: https://doi.org/10.4213/im306

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English version:
Izvestiya: Mathematics, 2000, 64:5, 1003–1015

Bibliographic databases:

MSC: 22E60, 14L30, 14D25, 15A72, 13A50, 20G15, 17B20
Received: 29.07.1999

Citation: D. D. Pervouchine, “Invariants and orbits of the standard $(\mathrm SL_4(\mathbb C)\times\mathrm SL_4(\mathbb C)\times\mathrm SL_2(\mathbb C))$-module”, Izv. RAN. Ser. Mat., 64:5 (2000), 133–146; Izv. Math., 64:5 (2000), 1003–1015

Citation in format AMSBIB
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\pages 133--146
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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. D. D. Pervouchine, “On the closures of orbits of fourth order matrix pencils”, Izv. Math., 66:5 (2002), 1047–1055  mathnet  crossref  crossref  mathscinet  zmath
    2. Pervouchine D.D., “Hierarchy of closures of matrix pencils”, J. Lie Theory, 14:2 (2004), 443–479  mathscinet  zmath  isi
    3. de Graaf W.A., “Computing representatives of nilpotent orbits of theta-groups”, J Symbolic Comput, 46:4 (2011), 438–458  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. De Graaf W.A., Oriente F., “Classifying Semisimple Orbits of Theta-Groups”, Math. Comput., 83:289 (2014), 2509–2526  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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