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

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- by Ian M. Musson
- Represent. Theory
**1**(1997), 405-423 - DOI: https://doi.org/10.1090/S1088-4165-97-00020-4
- Published electronically: November 17, 1997
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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.## References

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## Bibliographic Information

**Ian M. Musson**- Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413
- MR Author ID: 189473
- Email: musson@csd.uwm.edu
- 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.
- © Copyright 1997 American Mathematical Society
- Journal: Represent. Theory
**1**(1997), 405-423 - MSC (1991): Primary 17B35
- DOI: https://doi.org/10.1090/S1088-4165-97-00020-4
- MathSciNet review: 1479886