### 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 2008 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Advances in Applied Mathematics*,

*40*(4), 514-535. https://doi.org/10.1016/j.aam.2007.05.003

**Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1).** / Ikeda, Takeshi; Mizukawa, Hiroshi; Nakajima, Tatsuhiro; Yamada, Hiro Fumi.

Research output: Contribution to journal › Article

*Advances in Applied Mathematics*, vol. 40, no. 4, pp. 514-535. https://doi.org/10.1016/j.aam.2007.05.003

}

TY - JOUR

T1 - Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A1(1)

AU - Ikeda, Takeshi

AU - Mizukawa, Hiroshi

AU - Nakajima, Tatsuhiro

AU - Yamada, Hiro Fumi

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - Boson-fermion correspondence

KW - Schur function

KW - Schur's Q-function

UR - http://www.scopus.com/inward/record.url?scp=42049112143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42049112143&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2007.05.003

DO - 10.1016/j.aam.2007.05.003

M3 - Article

AN - SCOPUS:42049112143

VL - 40

SP - 514

EP - 535

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

IS - 4

ER -