  J. Lepowsky and R. L. Wilson initiated the approach to combinatorial
Rogers-Ramanujan type identities via the vertex operator constructions of
representations of affine Lie algebras. In a joint work with Arne Meurman this
approach is developed further in the framework of vertex operator algebras. The
main ingredients of that construction are defining relations for standard
modules and relations among them. The arguments involve both representation
theory and combinatorics, the final results hold only for affine Lie algebras
$A_1^{(1)}$ and $A_2^{(1)}$. In the present paper some of those arguments are
formulated and extended for general affine Lie algebras. The main result is a
kind of rank theorem, guaranteeing the existence of combinatorial relations
among relations, provided that certain purely combinatorial quantities are
equal to dimensions of certain representation spaces. Although the result holds
in quite general setting, applications are expected mainly for standard modules
of affine Lie algebras.
