Level one representations of the twisted affine algebras \(A^{(2)}_ n\) and \(D^{(2)}_ n\) (Q1200443)

During the last decade vertex operator realizations of integrable highest weight representations of affine Lie algebras have played an important role. It is known that each vertex operator realization of the level one representations depends on the choice of the Heisenberg subalgebra of the corresponding affine Lie algebra. Thus the number of distinct realizations equals to the number of inequivalent (i.e. nonconjugate under the adjoint action of the associated Kac-Moody group) Heisenberg subalgebras of the corresponding affine Lie algebra. In this paper the authors give vertex operator realizations of the level one representations for the twisted affine Lie algebras \(A_ n^{(2)}\) and \(D_ n^{(2)}\) corresponding to each inequivalent Heisenberg subalgebra.