Combinatorial bases of basic modules for affine Lie algebras C_n^{(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\mathfrak{sl}(2,\mathbb{C})^{\sim} 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^{(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^{(1)}.

Mirko Primc and Tomislav Šikić, Combinatorial bases of basic modules for affine Lie algebras C_n^{(1)}, J. Math. Phys. 57, 091701 (2016); http://dx.doi.org/10.1063/1.4962392.