Generalised Verma modules for the orthosymplectic Lie superalgebra ospk|2

The composition factors with their multiplicities and the submodule lattices are determined for generalised Verma modules over the orthosymplectic Lie superalgebra ospk|2. The results enable us to obtain explicit formulae for the formal characters and dimensions of the finite-dimensional irreducible modules. Applying these results, we also compute the first and second cohomology groups of the Lie superalgebra with coefficients in finite-dimensional Kac modules and irreducible modules.