Annihilating fields of standard modules of sl(2,C)(similar to) and combinatorial identities

We show that a set of local admissible fields generates a vertex algebra. F or an affine Lie algebra (g) over tilde we construct the corresponding leve l Ic vertex operator algebra and we show that level k highest weight (g) ov er tilde-modules are modules for this vertex operator algebra. We determine the set of annihilating fields of level k standard modules and we study th e corresponding loop (g) over tilde module-the set of relations that define s standard modules. In the case when (g) over tilde is of type A(1)((1)), w e construct bases of standard modules parameterized by colored partitions a nd, as a consequence, we obtain a series of Rogers-Ramanujan type combinato rial identities.