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Irreducible representations of solvable Lie superalgebras

Author(s): Alexander Sergeev
Journal: Represent. Theory 3 (1999), 435-443.
MSC (1991): Primary 17A70; Secondary 17B30
Posted: November 9, 1999
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Abstract: The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V. Kac is refined. In reality these representations are not just induced from a polarization but are twisted ones, as infinite dimensional representations of solvable Lie algebras. Various cases of irreducibility (general and of type Q) are classified.

References:

[BL]
Bernstein J. and Leites D., The superalgebra $Q(n)$, the odd trace and the odd determinant, C. R. Acad. Bulgare Sci. 35 (1982), no. 3, 285-286. MR 84c:17003

[D]
Dixmier J., Enveloping algebras, Revised reprint of the 1977 translation, Graduate Studies in Mathematics, 11, American Mathematical Society, Providence, RI, 1996. MR 97c:17010

[K]
Kac V., Lie superalgebras, Adv. Math. 26 (1977), 8-96. MR 58:5803

[L]
Leites D. (ed.), Seminar on supermanifolds #22, Reports of the Department of Mathematics of Stockholm University, 1988-4, 1-12.

[Shch]
Shchepochkina I. M., Maximal solvable subalgebras of the Lie superalgebras ${{\mathfrak{gl}}}(m\vert n)$ and ${{\mathfrak{sl}}}(m\vert n)$. (Russian) Funktsional. Anal. i Prilozhen. 28 (1994), no. 2, 92-94; translation in Functional Anal. Appl. 28 (1994), no. 2, 147-149. MR 95b:17013

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Additional Information:

Alexander Sergeev
Affiliation: On leave of absence from Balakovo Institute of Technique of Technology and Control, Branch of Saratov State Technical University, Russia - Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden
Email: mleites@matematik.su.se (subject: for Sergeev)

DOI: 10.1090/S1088-4165-99-00086-2
PII: S 1088-4165(99)00086-2
Keywords: Solvable Lie superalgebras
Received by editor(s): November 4, 1998
Received by editor(s) in revised form: September 8, 1999
Posted: November 9, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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