Realization of level one representations of U q(g) at a root of unity

Abstract

Using vertex operators, we construct explicitly Lusztig's ℤ[q,q^−4]-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one irreducible modules at roots of unity and show that the character is given by the Weyl-Kac character formula.