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Representation Theory

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Irreducible representations of solvable Lie superalgebras

Author: Alexander Sergeev
Journal: Represent. Theory 3 (1999), 435-443
MSC (1991): Primary 17A70; Secondary 17B30
Published electronically: November 9, 1999
MathSciNet review: 1722111
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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.

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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, Krรคftriket hus 6, S-106 91, Stockholm, Sweden
Email: (subject: for Sergeev)

Keywords: Solvable Lie superalgebras
Received by editor(s): November 4, 1998
Received by editor(s) in revised form: September 8, 1999
Published electronically: November 9, 1999
Article copyright: © Copyright 1999 American Mathematical Society