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J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorialRogers-Ramanujan type identities via vertex operator constructions of standard(i.e. integrable highest weight) representations of affine Kac-Moody Liealgebras. A.~Meurman and M.~Primc developed further this approach for$\mathfrak{sl}(2,\mathbb C)\widetilde{}\ $ by using vertex operator algebrasand Verma modules. In this paper we use the same method to constructcombinatorial bases of basic modules for affine Lie algebras of type$C_{n}\sp{(1)}$ and, as a consequence, we obtain a series of Rogers-Ramanujantype identities. A major new insight is a combinatorial parametrization ofleading terms of defining relations for level one standard modules for affineLie algebra of type $C_{n}\sp{(1)}$.

Combinatorial bases of basic modules for $C_{n}\sp{(1)}$