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Representation Theory

ISSN 1088-4165

 
 

 

The enveloping algebra of the Lie
superalgebra $osp(1,2r)$


Author: Ian M. Musson
Journal: Represent. Theory 1 (1997), 405-423
MSC (1991): Primary 17B35
DOI: https://doi.org/10.1090/S1088-4165-97-00020-4
Published electronically: November 17, 1997
MathSciNet review: 1479886
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Abstract: Let $\mathfrak{g}$ be the Lie superalgebra $osp(1,2r)$ and $U(\mathfrak{g})$ the enveloping algebra of $\mathfrak{g}$.

In this paper we obtain a description of the set of primitive ideals Prim $\! U(\mathfrak{g})$ as an ordered set. We also obtain the multiplicities of composition factors of Verma modules over $U(\mathfrak{g})$, and of simple highest weight modules for $\! U(\mathfrak{g})$ when regarded as a $U(\mathfrak{g}_{0})$-module by restriction.


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Additional Information

Ian M. Musson
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413
Email: musson@csd.uwm.edu

DOI: https://doi.org/10.1090/S1088-4165-97-00020-4
Received by editor(s): January 27, 1997
Received by editor(s) in revised form: July 25, 1997
Published electronically: November 17, 1997
Additional Notes: Research partially supported by National Science Foundation grant DMS 9500486.
Article copyright: © Copyright 1997 American Mathematical Society