Trivial module for ortho-symplectic Lie superalgebras and Littlewood's formula

We show that the denominator identity for ortho-symplectic Lie superalgebras osp(k{pipe}2n) is equivalent to the Littlewood's formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for osp(k{pipe}2n). Furthermore, we discuss the harmonic representative elements of the Kostant's u-cohomology with trivial coefficients.