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

Orlando Alvarez, Paul Windey, Michelangelo Mangano

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4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)317-331
Number of pages15
JournalNuclear Physics, Section B
Issue numberC
StatePublished - 1986
Externally publishedYes


ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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