Differential operator realizations of superalgebras and free field representations of corresponding current algebras

Based on the particular orderings introduced for the positive roots of finite-dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the osp(2r|2n) and osp(2r+1|2n) superalgebras and the explicit free field realizations of the corresponding current superalgebras osp(2r|2n)k and osp(2r+1|2n)k at an arbitrary level k. The free field representations of the corresponding energy-momentum tensors and screening currents of the first kind are also presented.