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.
"Realization of level one representations of at a root of unity." Duke Math. J. 108 (1) 183 - 197, 15 May 2001. https://doi.org/10.1215/S0012-7094-01-10816-8