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Mathematics of the USSR-Sbornik, 1985, Volume 51, Issue 2, Pages 419–427
DOI: https://doi.org/10.1070/SM1985v051n02ABEH002867
(Mi sm2029)
 

This article is cited in 131 scientific papers (total in 131 papers)

The tensor algebra of the identity representation as a module over the Lie superalgebras $\mathfrak Gl(n,m)$ and $Q(n)$

A. N. Sergeev
References:
Abstract: Let $T$ be the tensor algebra of the identity representation of the Lie superalgebras in the series $\mathfrak Gl$ and $Q$. The method of Weyl is used to construct a correspondence between the irreducible representations (respectively, the irreducible projective representations) of the symmetric group and the irreducible $\mathfrak Gl$- (respectively, $Q$-) submodules of $T$. The properties of the representations are studied on the basis of this correspondence. A formula is given for the characters on the irreducible $Q$-submodules of $T$.
Bibliography: 8 titles.
Received: 22.04.1983
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1984, Volume 123(165), Number 3, Pages 422–430
Bibliographic databases:
UDC: 512
MSC: Primary 17A70, 17B10; Secondary 15A72, 20C30
Language: English
Original paper language: Russian
Citation: A. N. Sergeev, “The tensor algebra of the identity representation as a module over the Lie superalgebras $\mathfrak Gl(n,m)$ and $Q(n)$”, Mat. Sb. (N.S.), 123(165):3 (1984), 422–430; Math. USSR-Sb., 51:2 (1985), 419–427
Citation in format AMSBIB
\Bibitem{Ser84}
\by A.~N.~Sergeev
\paper The tensor algebra of the identity representation as a~module over the Lie superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 3
\pages 422--430
\mathnet{http://mi.mathnet.ru/sm2029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=735715}
\zmath{https://zbmath.org/?q=an:0573.17002}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 419--427
\crossref{https://doi.org/10.1070/SM1985v051n02ABEH002867}
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  • https://www.mathnet.ru/eng/sm/v165/i3/p422
  • This publication is cited in the following 131 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:2139
    Russian version PDF:534
    English version PDF:63
    References:106
     
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