### 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.

Original language | English |
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Pages (from-to) | 514-535 |

Number of pages | 22 |

Journal | Advances in Applied Mathematics |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 1 2008 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Ikeda, T., Mizukawa, H., Nakajima, T., & Yamada, H. F. (2008). Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A

_{1}^{(1)}.*Advances in Applied Mathematics*,*40*(4), 514-535. https://doi.org/10.1016/j.aam.2007.05.003