2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135106Given an affine Kac-Moody Lie algebra $\tilde{\mathfrak{g}}[σ]$ of arbitrary type, we determine certain minimal sets of annihilating fields of standard $\tilde{\mathfrak{g}}[σ]$-modules. We then use these sets in order to obtain a characterization of standard $\tilde{\mathfrak{g}}[σ]$-modules in terms of irreducible loop $\tilde{\mathfrak{g}}[σ]$-modules, which proves to be a useful tool for combinatorial constructions of bases for standard $\tilde{\mathfrak{g}}[σ]$-modules.15 pages, no figures, LaTeX. To appear in Mathematische ZeitschriftQuantum AlgebraPrimary: 17B67, 17B69; Secondary: 81R10text