## 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 |
---|---|

Pages (from-to) | 514-535 |

Number of pages | 22 |

Journal | Advances in Applied Mathematics |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2008 May |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Applied Mathematics

## Fingerprint

Dive into the research topics of 'Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_{1}

^{(1)}'. Together they form a unique fingerprint.