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Transactions of the American Mathematical Society

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On the structure of weight modules


Authors: Ivan Dimitrov, Olivier Mathieu and Ivan Penkov
Journal: Trans. Amer. Math. Soc. 352 (2000), 2857-2869
MSC (2000): Primary 17B10
DOI: https://doi.org/10.1090/S0002-9947-00-02390-4
Published electronically: February 28, 2000
Erratum: Trans. Amer. Math. Soc. 356 (2004), 3403-3404.
MathSciNet review: 1624174
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Abstract | References | Similar Articles | Additional Information

Abstract: Given any simple Lie superalgebra ${\mathfrak{g}}$, we investigate the structure of an arbitrary simple weight ${\mathfrak{g}}$-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W$(n)$. Most of them are simply Levi subalgebras of ${\mathfrak{g}}_{0}$, in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.


References [Enhancements On Off] (What's this?)

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Additional Information

Ivan Dimitrov
Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
Address at time of publication: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Email: dimitrov@math.ucla.edu

Olivier Mathieu
Affiliation: Université Louis Pasteur, IRMA, 7 rue René Descartes, 67000 Strasbourg, France
Email: mathieu@math.u-strasbg.fr

Ivan Penkov
Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
Email: penkov@math.ucr.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02390-4
Received by editor(s): October 8, 1997
Published electronically: February 28, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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