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

Abstract

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