Level one representations of the twisted affine algebras A_n^(2) and D

Level one representations of the twisted affine algebras A_n^(2) and D_n^(2)

Abstract

We give an explicit description of the Kac-Peterson-Lepowsky construction of the level one representations for the twisted affine Lie algebras A_n^(2) and D_n^(2). We assign to any conjugacy class of the Weyl group of A_n and D_n 1) an equivalent class of maximal Heisenberg subalgebras of the corresponding twisted affine Lie algebras, and 2) 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.