  We show that a set of local admissible fields generates a vertex algebra. For
an affine Lie algebra $\tilde\goth g$ we construct the corresponding level $k$
vertex operator algebra and we show that level $k$ highest weight $\tilde\goth
g$-modules are modules for this vertex operator algebra. We determine the set
of annihilating fields of level $k$ standard modules and we study the
corresponding loop $\tilde\goth g$ module---the set of relations that defines
standard modules. In the case when $\tilde\goth g$ is of type $A_1^{(1)}$, we
construct bases of standard modules parameterized by colored partitions and, as
a consequence, we obtain a series of Rogers-Ramanujan type combinatorial
identities.
