Combinatorial bases of basic modules for affine Lie algebras Cn(1)

Abstract

Lepowsky and 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. Meurman and Primc developed further this approach for sl(2,C) ˜ 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 Cn(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 Cn(1).