  Formulas are obtained that express the Schur S-functions indexed by Young
diagrams of rectangular shape as linear combinations of "mixed" products of
Schur's S- and Q-functions. The proof is achieved by using representations of
the affine Lie algebra of type A_1^{(1)}. A realization of the basic
representation that is of ``D_2^{(2)}''-type plays the central role.
