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Mosc. Math. J., 2008, Volume 8, Number 1, Pages 91–109 (Mi mmj5)  

This article is cited in 4 scientific papers (total in 4 papers)

On representations of the affine superalgebra $\mathbb q(n)^{(2)}$

M. Gorelika, V. V. Serganovab

a Weizmann Institute of Science
b University of California, Berkeley

Abstract: In this paper we study highest weight representations of the affine Lie superalgebra $\mathbb q(n)^{(2)}$. We prove that any Verma module over this algebra is reducible and calculate the character of an irreducible $\mathbb q(n)^{(2)}$-module with a generic highest weight. This formula is analogous to the Kac–Kazhdan formula for generic irreducible modules over affine Lie algebras at the critical level.

Key words and phrases: Affine Lie superalgebra, highest weight representation, Shapovalov form.

Full text: http://www.ams.org/.../abst8-1-2008.html
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Bibliographic databases:

MSC: 32S50
Received: October 2, 2006
Language: English

Citation: M. Gorelik, V. V. Serganova, “On representations of the affine superalgebra $\mathbb q(n)^{(2)}$”, Mosc. Math. J., 8:1 (2008), 91–109

Citation in format AMSBIB
\Bibitem{GorSer08}
\by M.~Gorelik, V.~V.~Serganova
\paper On representations of the affine superalgebra $\mathbb q(n)^{(2)}$
\jour Mosc. Math.~J.
\yr 2008
\vol 8
\issue 1
\pages 91--109
\mathnet{http://mi.mathnet.ru/mmj5}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2422268}
\zmath{https://zbmath.org/?q=an:1162.17023}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261829600005}


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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. A. V. Lebedev, D. A. Leites, “Shapovalov determinant for loop superalgebras”, Theoret. and Math. Phys., 156:3 (2008), 1292–1307  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Chen H., Guay N., “Twisted Affine Lie Superalgebra of Type Q and Quantization of its Enveloping Superalgebra”, Math. Z., 272:1-2 (2012), 317–347  crossref  mathscinet  zmath  isi  scopus
    3. Luo C.L., “on Polynomial Representations of Strange Lie Superalgebras of Q-Type”, Acta. Math. Sin.-English Ser., 32:5 (2016), 559–570  crossref  mathscinet  zmath  isi  scopus
    4. Calixto L., Moura A., Savage A., “Equivariant Map Queer Lie Superalgebras”, Can. J. Math.-J. Can. Math., 68:2 (2016), 258–279  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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