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

Musson, Ian

doi:10.1090/S1088-4165-97-00020-4

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.

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