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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 2(10), Pages 259–274 (Mi msb2673)  

This article is cited in 6 scientific papers (total in 6 papers)

Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras

A. V. Shapovalov


Abstract: We describe all of the irreducible representations of the simple algebras of the series $H(n)$, and we realize these representations either as irreducible induced representations of a Lie subalgebra of $H(n)$ or as subrepresentations of the representation of the Hamiltonian vector fields in the space of differential forms on a supermanifold; these cases are mutually exclusive.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:4, 541–554

Bibliographic databases:

UDC: 519.46
MSC: Primary 17E05, 17B10; Secondary 17B20, 17B55, 58A15, 58F05
Received: 03.03.1978

Citation: A. V. Shapovalov, “Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras”, Mat. Sb. (N.S.), 107(149):2(10) (1978), 259–274; Math. USSR-Sb., 35:4 (1979), 541–554

Citation in format AMSBIB
\Bibitem{Sha78}
\by A.~V.~Shapovalov
\paper Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 2(10)
\pages 259--274
\mathnet{http://mi.mathnet.ru/msb2673}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=512011}
\zmath{https://zbmath.org/?q=an:0421.17003|0401.17008}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 541--554
\crossref{https://doi.org/10.1070/SM1979v035n04ABEH001571}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JJ04900007}


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  • http://mi.mathnet.ru/eng/msb/v149/i2/p259

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. A. Leites, “Formulas for the characters of irreducible finite-dimensional representations of simple Lie superalgebras”, Funct. Anal. Appl., 14:2 (1980), 106–109  mathnet  crossref  mathscinet  zmath
    2. Alexeevskij D., Leites D., Shchepochkina I., “Examples of Simple Infinite-Dimensional Lie-Superalgebras of Vector-Fields”, 33, no. 9, 1980, 1187–1190  mathscinet  isi
    3. G. S. Shmelev, “Invariant operators on a symplectic supermanifold”, Math. USSR-Sb., 48:2 (1984), 521–533  mathnet  crossref  mathscinet  zmath
    4. G. S. Shmelev, “$H(2n,m)$-invariant differential operators and irreducible $\operatorname{osp}(2,2n)$-representations”, Funct. Anal. Appl., 17:4 (1983), 323–325  mathnet  crossref  mathscinet  zmath  isi
    5. Yu. Yu. Kochetkov, “Singular vectors and discrete modules”, Russian Math. Surveys, 41:5 (1986), 145–146  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Pavel Grozman, Dimitry Leites, “The Shapovalov Determinant for the Poisson Superalgebras”, Journal of Nonlinear Mathematical Physics, 8:2 (2001), 220  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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