### Abstract

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra A^{(2)}_{2} are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

Original language | English |
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Pages (from-to) | 1317-1331 |

Number of pages | 15 |

Journal | Letters in Mathematical Physics |

Volume | 104 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2014 |

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Mizukawa, H., Nakajima, T., Seno, R., & Yamada, H. F. (2014). Schur Function Identities Arising From the Basic Representation of A

^{(2)}_{2}.*Letters in Mathematical Physics*,*104*(10), 1317-1331. https://doi.org/10.1007/s11005-014-0717-y