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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 120–137 (Mi znsl6615)  
This article is cited in 3 scientific papers (total in 3 papers)

Explicit equations for exterior square of the general linear group

R. A. Lubkova, I. I. Nekrasovb

a Mathematics and Mechanics Faculty, St. Petersburg State University, St. Petersburg, Russia
b Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (355 kB) Citations (3)
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Abstract: We present several explicit systems of equations defining exterior square of the general linear group $\wedge^2\mathrm{GL}_n$ as an affine group scheme. Algebraic ingredients of the equations, exterior numbers, are translated into the language of weight diagrams corresponding to Lie groups of type $A_{n-1}$ in representation with the highest weight $\varpi_2$.
Key words and phrases: general linear group, weight diagrams, exterior square.
Funding agency Grant number
Russian Science Foundation 17-11-01261
16-11-10200
Gazprom Neft
Received: 01.03.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 4, Pages 583–594
DOI: https://doi.org/10.1007/s10958-019-04559-5
Bibliographic databases:
Document Type: Article
UDC: 512.743.7
Language: Russian
Citation: R. A. Lubkov, I. I. Nekrasov, “Explicit equations for exterior square of the general linear group”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 120–137; J. Math. Sci. (N. Y.), 243:4 (2019), 583–594
Citation in format AMSBIB
\Bibitem{LubNek18}
\by R.~A.~Lubkov, I.~I.~Nekrasov
\paper Explicit equations for exterior square of the general linear group
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 120--137
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6615}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 4
\pages 583--594
\crossref{https://doi.org/10.1007/s10958-019-04559-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074847703}
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  • https://www.mathnet.ru/eng/znsl/v470/p120
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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