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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79125Using 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 then realize the level one irreducible modules at roots of unity and show that the q-dimension is still given by the Weyl-Kac character formula. As a consequence we also answer the corresponding question of realizing the affine Kac-Moody Lie algebras of simply laced type at level one in finite characteristic.13 pagesQuantum AlgebraRepresentation Theory17BRealization of level one representations of $U_q(\hat{\mathfrak g})$ at a root of unitytext