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

Vyjayanthi Chari, Naihuan Jing

Using vertex operators, we construct explicitly Lusztig's $\mathbb{Z}[q,q^{-1}]$-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We th…