  Reduction algebras are known by many names in the literature, including step
algebras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras,
to name a few. These algebras, realized by raising and lowering operators,
allow for the calculation of Clebsch-Gordan coefficients, branching rules, and
intertwining operators; and have connections to extremal equations and
dynamical R-matrices in integrable face models.
  In this paper we continue the study of the diagonal reduction superalgebra
$A$ of the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$. We construct
a Harish-Chandra homomorphism, Verma modules, and study the Shapovalov form on
each Verma module. Using these results, we prove that the ghost center (center
plus anti-center) of $A$ is generated by two central elements and one
anti-central element (analogous to the Scasimir due to Le\'{s}niewski for
$\mathfrak{osp}(1|2)$). As another application, we classify all
finite-dimensional irreducible representations of $A$. Lastly, we calculate an
infinite-dimensional tensor product decomposition explicitly.
