Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1)

Takeshi Ikeda, Hiroshi Mizukawa, Tatsuhiro Nakajima, Hiro Fumi Yamada

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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.

Original languageEnglish
Pages (from-to)514-535
Number of pages22
JournalAdvances in Applied Mathematics
Issue number4
Publication statusPublished - May 1 2008



  • Boson-fermion correspondence
  • Schur function
  • Schur's Q-function

ASJC Scopus subject areas

  • Applied Mathematics

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