Bosonic and fermionic realizations
of the affine algebra so(2n)
Abstract
We give an explicit description of the Kac-Peterson-Lepowsky construction of the
basic representation for the affine Lie algebra so(2n).
Using the conjugacy classes of the Weyl group of so(2n), we describe
all inequivalent maximal Heisenberg subalgebras (HSA's) of the corresponding
affine Lie algebra. We associate to these HSA's multicomponent charged and
neutral free fermionic fields. The boson-fermion correspondence for
these fields provides us with fermionic vertex operators, whose `normal
ordered products' give the (twisted) vertex operators of the
Kac-Peterson-Lepowsky construction.