  We study the crossing symmetry of the conformal blocks of the conformal field
theory based on the affine Lie superalgebra osp(1|2). Within the framework of a
free field realization of the osp(1|2) current algebra, the fusion and braiding
matrices of the model are determined. These results are related in a simple way
to those corresponding to the su(2) algebra by means of a suitable
identification of parameters. In order to obtain the link invariants
corresponding to the osp(1|2) conformal field theory, we analyze the
corresponding topological Chern-Simons theory. In a first approach we quantize
the Chern-Simons theory on the torus and, as a result, we get the action of the
Wilson line operators on the supercharacters of the affine osp(1|2). From this
result we get a simple expression relating the osp(1|2) polynomials for torus
knots and links to those corresponding to the su(2) algebra. Further, this
relation is verified for arbitrary knots and links by quantizing the
Chern-Simons theory on the punctured two-sphere.
