Mixed expansion formula for the rectangular Schur functions and the   affine Lie algebra A_1^(1)
  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. 
Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima and Hiro-Fumi   Yamada