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.
ASJC Scopus subject areas
- Nuclear and High Energy Physics