### 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 |
---|---|

Pages (from-to) | 1317-1331 |

Number of pages | 15 |

Journal | Letters in Mathematical Physics |

Volume | 104 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

^{(2)}

_{2}.

*Letters in Mathematical Physics*,

*104*(10), 1317-1331. https://doi.org/10.1007/s11005-014-0717-y

**Schur Function Identities Arising From the Basic Representation of A ^{(2)}_{2}.** / Mizukawa, Hiroshi; Nakajima, Tatsuhiro; Seno, Ryoji; Yamada, Hiro Fumi.

Research output: Contribution to journal › Article

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_{2}',

*Letters in Mathematical Physics*, vol. 104, no. 10, pp. 1317-1331. https://doi.org/10.1007/s11005-014-0717-y

^{(2)}

_{2}. Letters in Mathematical Physics. 2014;104(10):1317-1331. https://doi.org/10.1007/s11005-014-0717-y

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TY - JOUR

T1 - Schur Function Identities Arising From the Basic Representation of A(2)2

AU - Mizukawa, Hiroshi

AU - Nakajima, Tatsuhiro

AU - Seno, Ryoji

AU - Yamada, Hiro Fumi

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Boson-fermion correspondence

KW - Schur function

KW - Schur's Q-function

UR - http://www.scopus.com/inward/record.url?scp=84906825197&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906825197&partnerID=8YFLogxK

U2 - 10.1007/s11005-014-0717-y

DO - 10.1007/s11005-014-0717-y

M3 - Article

VL - 104

SP - 1317

EP - 1331

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 10

ER -