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

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.