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

TL;DR

This paper constructs combinatorial bases for basic modules of affine Lie algebras of type C_n^{(1)} using vertex operator methods, leading to new Rogers-Ramanujan type identities and a combinatorial parametrization of relations.

Contribution

It extends vertex operator algebra techniques to type C_n^{(1)} affine Lie algebras, providing new combinatorial bases and identities.

Findings

Constructed combinatorial bases for basic modules of type C_n^{(1)}.

Derived Rogers-Ramanujan type identities from these bases.

Provided a new combinatorial parametrization of relations for level one modules.

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 $C_{n}\sp{(1)}$.