Combinatorial relations among relations of $C_{2}\sp{(1)}$-standard modules for higher levels

Abstract

For an affine Lie algebra $\hat{\mathfrak g}$ the coefficients of certain vertex operators which annihilate level $k$ standard $\hat{\mathfrak g}$-modules are the defining relations for level $k$ standard modules. In the paper \cite{PS3} combinatorial structure of the leading terms of mentioned relations for level $k=2$ standard $\hat{\mathfrak g}$-modules and affine Lie algebras of type $C_{n}\sp{(1)}$ is given. The main result of this paper is a construction of combinatorially parameterized relations among relations of $C_{2}\sp{(1)}$-standard modules for all levels.