Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1)
Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima, Hiro-Fumi Yamada
Abstract
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 A1(1). A realization of the basic representation that is of ``D2(2)''-type plays the central role.
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