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

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.