Ghost center and representations of the diagonal reduction algebra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:mi mathvariant="fraktur">osp</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">|</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>

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