### Abstract

An explicit representation of the B_{n}
^{(1)} affine Lie algebra (Kac-Moody algebra) is constructed in terms of vertex operators associated with the Chevalley basis of the underlyingfinite-dimentsionnal Lie algebra. This construction, contrary to the simpler current algebra one, gives a concrete realization of the spinor representation of the algebra. The key feature is a partial bosonization of two-dimensional Weyl-Majorana free fermions. The vertex operators associated with the long and short roots of the B_{n} algebra have fermion number zero and one, respectively.

Original language | English (US) |
---|---|

Pages (from-to) | 317-331 |

Number of pages | 15 |

Journal | Nuclear Physics B |

Volume | 277 |

Issue number | C |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*277*(C), 317-331. https://doi.org/10.1016/0550-3213(86)90444-X

**Vertex operator construction of the SO(2n+1) Kac-Moody algebra and its spinor representation.** / Alvarez, Orlando; Windey, Paul; Mangano, Michelangelo.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 277, no. C, pp. 317-331. https://doi.org/10.1016/0550-3213(86)90444-X

}

TY - JOUR

T1 - Vertex operator construction of the SO(2n+1) Kac-Moody algebra and its spinor representation

AU - Alvarez, Orlando

AU - Windey, Paul

AU - Mangano, Michelangelo

PY - 1986

Y1 - 1986

N2 - An explicit representation of the Bn (1) affine Lie algebra (Kac-Moody algebra) is constructed in terms of vertex operators associated with the Chevalley basis of the underlyingfinite-dimentsionnal Lie algebra. This construction, contrary to the simpler current algebra one, gives a concrete realization of the spinor representation of the algebra. The key feature is a partial bosonization of two-dimensional Weyl-Majorana free fermions. The vertex operators associated with the long and short roots of the Bn algebra have fermion number zero and one, respectively.

AB - An explicit representation of the Bn (1) affine Lie algebra (Kac-Moody algebra) is constructed in terms of vertex operators associated with the Chevalley basis of the underlyingfinite-dimentsionnal Lie algebra. This construction, contrary to the simpler current algebra one, gives a concrete realization of the spinor representation of the algebra. The key feature is a partial bosonization of two-dimensional Weyl-Majorana free fermions. The vertex operators associated with the long and short roots of the Bn algebra have fermion number zero and one, respectively.

UR - http://www.scopus.com/inward/record.url?scp=24544466811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24544466811&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(86)90444-X

DO - 10.1016/0550-3213(86)90444-X

M3 - Article

AN - SCOPUS:24544466811

VL - 277

SP - 317

EP - 331

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - C

ER -