Annihilating fields of standard modules for affine Lie algebras

Given an affine Kac-Moody Lie algebra (g) over tilde[sigma] of arbitrary type, we determine certain minimal sets of annihilating fields of standard (g) over tilde[sigma]-modules. We then use these sets in order to obtain a characterization of standard (g) over tilde[sigma]-modules in terms of irreducible loop (g) over tilde[sigma]-modules, which proves to be a useful tool for combinatorial constructions of bases for standard (g) over tilde[sigma]-modules.