Realization of level one representations of \(U_q(\hat{\mathfrak g})\) at a root of unity (Q1847837)

By using the vertex operator construction [\textit{I. B. Frenkel} and \textit{N. Jing}, Proc. Natl. Acad. Sci. USA 85, 9373--9377 (1988; Zbl 0662.17006)] the authors construct explicitly Lusztig's \(\mathbb Z[q,q^{-1}]\)-lattice, studied in [\textit{G. Lusztig}, Introduction to Quantum Groups, Prog. Math. 110, Birkhäuser, Boston (1993; Zbl 0788.17010)], for the level one irreducible representations of quantum affine algebras of ADE type. Then the authors realize the level one irreducible modules at a primitive \(l\)th root of unity and show that the character is given by the Weyl-Kac character formula, provided that \(l\) is coprime to the Coxeter number of the underlying finite-dimensional Lie algebra.