Annihilating Fields Of Standard Modules Of Si(2, C) And Combinatorial Identities

Aims to show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\mathfrak g}$, this work constructs the corresponding level $k$ vertex operator algebra and shows that level $k$ highest weight $\tilde{\mathfrak g}$-modules are modules for this vertex operator algebra.