### 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) |
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Pages (from-to) | 317-331 |

Number of pages | 15 |

Journal | Nuclear Physics, Section B |

Volume | 277 |

Issue number | C |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

Alvarez, O., Windey, P., & Mangano, M. (1986). Vertex operator construction of the SO(2n+1) Kac-Moody algebra and its spinor representation.

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