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Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

Takeshi Ikeda·Hiroshi Mizukawa·Tatsuhiro Nakajima·Hiro-Fumi Yamada
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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 A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.

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Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima, Hiro-Fumi Yamada. 2007-04-10. Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1). https://arxiv.org/abs/math/0512257

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